[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass †Pteraspidomorphi Goodrich, 1909 [monotypic]
         Class †Pteraspidomorpha
           Subclass †Heterostraci Lankester, 1868
             Order †Traquairaspidiformes Stensio, 1958 [monotypic]
               Family †Traquairaspididae Kiaer, 1932, nom. praeval.
                 1 Genus †Traquairaspis Kiaer, 1932
                 2 Genus †Weigeltaspis Brotzen, 1933
                 3 Genus †Phialaspis Wills, 1935