ChordaTa

Subphylum Urochordata

Subphylum Cephalochordata

Subphylum Craniata

The classification of vertebrates is awful. Most of the standard groups - Agnatha, Osteichthyes, Sarcopterygii, Amphibia, Reptilia - are woefully paraphyletic and have either been abandoned or extended. The results, though, have not settled in and so we are left with a mess. Here's a tree to work from.

Myxini (hagfish)

Vertebrata

Petromyzontiformes (lampreys)

Various extinct forms

Gnathostoma

Placodermi - extinct

Chondrichthyes (cartiligenous fish)

Acanthodii - extinct

Osteichthyes

Actinopterygii (ray-finned fish)

Sarcopterygii

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)

Dinosauria

Various extinct forms

Aves (birds)