Omaha beach was a bungled situation. The bombers missed. The shore bombardment was of no effect. The amphibious tanks sank. So really, all that got ashore was light infantry, whilest the defenders (ironically, a large percentage weren't German) had heavy machine guns, direct and indirect fire cannons, and mortars.
A few cruisers did get close enough to the shore to provide direct fire. One cruiser, I cant remember if it was british or U.S., hit a mine, split in half, and sank almost immediately.
Of the prisoners that weren't shot immediately, it was found that there were Polish, Russians, and even some Asians manning the bunkers. In one case, as the Americans approached a bunker, a single gunshot was heard. The conscripted foreign troops shot the only German in there with them, and subsequently surrendered.