Re: what the classification of the snail

Snails have the following classifications:
Kingdom = Animalia
Phylum = Mollusca (which also includes mussels, clams, squid, octopusses, 
etc)
Class = Gastropoda (which includes all snails and slugs)

The common garden snail is further classified as such:
Subclass = Pulmonata (which includes all terrestrial snails and slugs 
because they use their mantle cavity as a type of "lung" and can breath 
air)
Order = Stylommatophora
Family = Helicidae
Genus and species = Helix aspersa

Aquatic snails are in the Subclass Prosobranchia and there are many Orders, 
Families, Genuses and species under this Subclass

Source: Brusca, R.C. and Brusca, G.J.  Invertebrates.  Sinauer Associates, 
Inc.  Sunderland, Mass. 1990