ChordaTa

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)