Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct. see Subphylum Vertebrata Cuvier, 1812
       Vertebrata (Lamarck, 1801) - vertebrates see Subphylum Vertebrata Cuvier, 1812
         Superclass †Pteraspidomorphi Goodrich, 1909 [monotypic]
           Class †Pteraspidomorphi Goodrich, 1909
             Subclass †Heterostraci Lankester, 1868
               ?Order †Traquairaspidiformes Stensio, 1958
                 1 Genus †Phialaspis Wills, 1935
                 2 Genus †Toombsaspis Tarrant, 1991
                 3 Genus †Traquairaspis Kiaer, 1932