There are THREE (3) phyla or categories of fish.
These phyla are:
1) Agnatha - jawless fish ; around 50 species in the world
2) Chrondrichthyes - cartilaginous fish ; around 600 species in the world
3) Osteichthyes - bony fish (divided into ray finned group and lobe finned group) ; around 30,000 species in the world.