What prompted Yamaguchi to split his airgroup when attacking the Americans at Midway?

Hiryu had been stiken by Lieutnant Lofton Henderson. Hi bomber crashed on the deck of the carrier, forcing the ship to repair apart from the main fleet.

Repair teams were efficient, but could not manage to allow a full scale-operating of the aircraft carrier, so it was decided to send airplanes in small groups, in accordance with the capabilities of launch.

Not to hijack the question asked, but merely in an effort to keep the story straight, please accept that Lofton Henderson was not a lieutenant, he was a Major, USMC, commanding VMSB-241 on Midway and led the the Marine dive bomber attack on the Japanese carrier force. He was shot down and killed in this attack.

An article in the “Marine Corps Gazette” Mar/Apr 1943 issue (page 36) entitled “Hats Off! To Marine Corps Aircraft Group 22” included this passage: “One of the Navy Crosses was awarded posthumously to Major Lofton R. Henderson, who was last seen crashing his burning scout-bomber on a Japanese carrier.”

The story of Henderson crashing into a Japanese carrier also appears in the “Bureau of Naval Personnel Information Bulletin” # 311, on page 52:
“All 84 pilots and aerial gunners of two Marine Corps squadrons have been awarded decorations for heroic achievement in the Battle of Midway. In addition, 58 ground crew men have won letters of commendation. . . . “One of the new awards, a Navy Cross, was made posthumously to Maj. Lofton R. Henderson, USMC, who crashed his flaming dive bomber into a Japanese carrier. . . . “They drove home glide-bombing runs on what is believed to have been the carrier Soryu. They went on down to between 500 and 300 feet-far below the usual releasing level-before dropping their bomb loads. Three direct hits were observed and several close misses. Smoke poured from the stern of the carrier. Each surviving gunner claimed at least one Zero fighter. “It was in this action that Major Henderson crashed his ship into the enemy carrier. His plane was set afire as he began his run on the target. But he did not waver. The crash was witnessed by the gunner of a plane which followed to within 300 feet of the carrier. . . .”

These two articles are not the only places one can find mention of Henderson crashing into a Japanese carrier. Gilbert Cant, on pages 228 and 229 of his America’s Navy in World War II (1944 edition), writes:
“Apparently Henderson’s squadron encountered a different portion of the enemy fleet from that which had been attacked previously, for the carrier which they made their principal target has been identified as the Soryu, which was neither one of the largest nor fastest in the enemy’s line. Concentrated anti-aircraft fire combined with fighter plane attacks to make the American planes’ approach extremely difficult. As leader of the squadron, Henderson was the first to bring his plane into position to begin his dive, and also the first to be fatally hit. Corporal Eugene T. Card, who was flying as gunner in another of the bombers reports that ‘The left wing of Major Henderson’s plane burst into flames. Despite this, he continued the attack and I saw him dive down the smokestack of the carrier. I am convinced it was deliberate.’”

On the other hand, of course, the funnels of Japanese carriers present tended to extend out from below the flight deck, out, and down which made them just a little difficult to dive down into.

Henderson’s citation for the posthumous award of the Navy Cross reads:

”The President of the United States of America takes pride in presenting the Navy Cross (Posthumously) to Major Lofton Russell Henderson (MCSN: 0-4084), United States Marine Corps, for extraordinary heroism and distinguished service in the line of his profession while serving as Squadron Commander and a Pilot in Marine Scout-Bombing Squadron TWO HUNDRED FORTY-ONE (VMSB-241), Marine Air Group TWENTY-TWO (MAG-22), Naval Air Station, Midway, during operations of the U.S. Naval and Marine Forces against the invading Japanese Fleet during the Battle of Midway on 4 June 1942. With utter disregard for his own personal safety, Major Henderson, with keen judgment and courageous aggressiveness in the face of strong enemy fighter opposition, led his squadron in an attack which contributed materially to the defeat of the enemy. He was subsequently reported as missing in action. It is believed he gallantly gave up his life in the service of his country.” See https://valor.militarytimes.com/hero/8368

No mention of crashing into a Japanese carrier.

And the historical record is clear in that none, not one, of the VMSB-241 SBDs or SB2Us inflicted any damage other than, perhaps, peppering with splinters and a strafing run. Nagumo’s report on the action clearly notes that three of Henderson’s planes scored three near misses astern of Kaga and four near Hiryu. Another dive bomber strafed Hiryu and killed four men, but that was the extent of the damage. See Robert Sherrod, History of Marine Corps Aviation in World War II, Combat Forces Press, 1952, page 60.

The Nagumo report, published by the USN ONI may be had from here https://www.ibiblio.org/hyperwar/Japan/IJN/rep/Midway/Nagumo/. Relevant damage charts can be found on page 54, click on the Hiryu link.

Certainly a gallant effort, but no material results and no one crashing his plane into any Japanese carrier.

I decided to delve into RAN archives (all of my investigations below are based on 'Chapter 3 – Australia's Coast Raided – Her Flanks Strengthened') which have the best overviews of the Pacific War as far as I can see. They don't go into massive detail regarding this, but it does clear up a few things, primarily, that Nagumo knew about enemy surface forces after 7.28 AM:

At this time Nagumo had no intimation of the near-presence of American aircraft carriers. At 7 a.m. he received a message from the commander of the Midway attacking aircraft saying that a second strike was needed—and in confirmation of that there followed immediately an attack on the carriers by Midway-based aircraft. It was a failure. Ten torpedo aircraft failed to secure a hit, and seven were shot down by the Japanese. But the attack, confirming the need of a second strike on Midway, and the lack of any report of American carriers in the vicinity, caused Nagumo to take a fateful decision. He had, in his four carriers, 93 aircraft standing by for instant launching against surface forces. He ordered them struck below to clear his flight decks for the recovery of the returning aircraft of the first Midway striking force—and for the torpedo aircrafts' armament to be changed to bombs for a second attack on the atoll.

So, when Nagumo organized the attacks against Midway he did not yet know of the carrier group steaming his way.

The first news of enemy surface forces reached Nagumo at 7.28 a.m., when a reconnaissance aircraft from the cruiser Tone reported ten ships, a report elaborated at 8.9 a.m. to "five cruisers and five destroyers", and given point at 8.20 a.m. with the amendment "the enemy is accompanied by what appears to be a carrier". By then Spruance had launched 116 aircraft—29 torpedo bombers, 67 dive bombers, and 20 fighters—from Hornet and Enterprise, which were steaming S.W. by W. at 25 knots in their wake towards the Japanese forces.

The success of this attack was primarily in diverting Japanese efforts from elsewhere given the number of American planes taken down:

Out of 41 torpedo aircraft from the three carriers, only six returned, and not a single torpedo reached the enemy ships. Yet

it was the stark courage and relentless drive of these young pilots of the obsolete torpedo planes that made possible the victory that followed. The radical manoeuvring that they imposed on the Japanese carriers prevented them from launching more planes. And the TBDs, by acting as magnets for the enemy's combat air patrol and pulling "Zekes" down to near water level, enabled the dive-bombing squadrons that followed a few minutes later to attack virtually unopposed by fighter planes, and to drop bombs on full deckloads in the process of being refuelled.

The later attack by Hiryu is, however, described below—although given the OP didn't include the time of the attack being asked about, I'm not sure this is the one that was meant. It is my reading, though it isn't explicitly said that looking at the efforts the Japanese fleet had to take previously to launch their planes (and then got hit badly even so), that Admiral Yamaguchi decided that any planes in the air attacking the enemy was better than no planes, overwhelming mass or not (and they achieved their goal as well, so he was right):

The fourth of Nagumo's carriers, Hiryu, had a few hours to live—and, during that time her aircraft, in two attacks, dive-bombing and torpedo, reduced Yorktown to a wreck. She remained afloat for some hours, but sank at 6 a.m. on 7th June, after having been torpedoed by the Japanese submarine I168 (which at the same time sank the destroyer Hammann) at 1.30 p.m. on the 6th.