See the map for 7-13 June https://www.backtonormandy.org/from-d-day-to-paris/3661-dday-plus-1-7.html

The 1st, 2nd and 29th Infantry Divisions attacked out of Omaha Beach to expand the beachhead and link up with their allies.

The 1st linked up with the British and pushed forward to Caumont-l’Êventé against weakening resistance.
The 29th fought its way south and west and linked up with forces from Utah Beach, while the 2nd attacked alongside both and secured the interval between them.
The 101st Airborne Division seized Carentan after fierce fighting, and the 82nd Airborne Division, subsequently reinforced by the 90th Infantry Division, faced similarly tough opposition expanding bridgeheads across the Merderet River.
The 4th Infantry Division battled its way along the coastline towards Montebourg, while Commonwealth Forces beat off fierce counterattacks around Caen.
Behind the expanding beachhead, an unrelenting buildup of troops and supplies continued.