ChordaTa

Subphylum Urochordata

Subphylum Cephalochordata

Subphylum Craniata

Vertebrate classification is awful. Most of the standard groups are paraphyletic, and so have either been extended (B) or abandoned. What's left is a mess that hasn't really settled into place yet. The following is a minimal tree including most traditionally class-level groups:

Myxini (hagfish)

Vertebrata

Petromyzontiformes (lampreys)

Various extinct forms

Gnathostoma

Placodermi - extinct

Chondrichthyes (cartiligenous fish)

Acanthodii - extinct

Osteichthyes B

Actinopterygii (ray-finned fish)

Sarcopterygii B

Various extinct forms

Coelocanthamorpha

Dipnoi (lungfish)

Tetrapoda

'Various extinct forms

Lissamphibia

Amniota

Synapsida

Various extinct forms

Mammalia

Anapsida

Various extinct forms

Chelonia (turtles)

Diapsida

Various extinct forms

Lepidosauromorpha

Various extinct forms

Squamata (lizards, snakes)

Sphenodontida (tuataras)

Archosauromorpha

Various extinct forms

Crocodylomorpha (crocodiles, alligators)

Aves (birds)