What is the classification of a rainbow trout?

It depends on which species you are talking about but they are of the Salmonidae family. Brown trout, sea troout, etc. have a differemt genus than others. They are of the Salmogenus with Atlantic Salmon. Rainbow Trout are of the Oncorhynchus genus. Brook Trout are found in the Char family or Salvelinus genus. Brook trout are my fav! Beautiful ain't they?:)