The troops in this first wave, known as Force O, were the 16th Infantry Regimental Combat Team of Maj. Gen. Clarence R. Huebner’s 1st Infantry Division—the Big Red One—which had already seen plenty of combat in North Africa and on Sicily. Attached to the 1st for most of the first day of this operation, known as “Overlord,” was the 116th Infantry Regimental Combat Team of Maj. Gen. Charles Gerhardt’s 29th Infantry Division—a well-trained division that had not yet experienced combat. The 16th, commanded by Colonel George A. Taylor, was scheduled to land on “Easy Red” and “Fox Green” beaches, two sections of a five-mile-long beachhead code-named “Omaha”; the 116th’s assigned sectors, just to the west of the 16th’s, were designated “Dog Green,” “Dog White,” and “Dog Red.”
https://warfarehistorynetwork.com/article/d-day-battle-for-easy-red-fox-green-beaches/
The 36th was worn out from fighting up through all of Italy and were given the easier beach.
https://texasmilitaryforcesmuseum.org/36division/archives/caval/green.htm