ChordaTa

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)