Think of the Halo 2 shotgun, now change the sights from green back to blue, and add a laser sight (I have no idea why Bungie put this on) on the left side in between the magazine and barrel.

I can't find a picture of a marine holding a shotgun, but looking at the size comparison in-game, the shotgun is almost as long as he is tall. There's no way it is 12-gauge. It has to be at least 10-gauge.