Lots of dogs snore but the longer the nose on a dog the less chance it'll snore loudly unless it has a very large chest. Brachycephalic breeds (breeds of dogs with "baby faces" or pushed in noses) snore because their noses are just too short for them to breathe properly and because they often have stenotic nares (very small nasal openings), elongated soft palates from the tissues of the throat and nose being compressed in the shorter muzzle area, tracheal stenosis (from the trachea or windpipe being narrowed in areas), and a host of other issues.
Dog breeds with large chest cavities may sound as though they are snoring (and some actually do) but often what you are hearing is the deep breath thrumming through their chests. Like humans they can have loud rumbling snores though due to some of the same problems that causes sleep apnea in humans.
One fun fact is that your dog, if you have raised it from young enough, can actually begin to breathe in rhythm with you and in volume if you happen to snore.