[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
         Class †Placodermi McCoy, 1848
           †Arthrodira Woodward, 1891
             Order †Phlyctaeniiformes
               Suborder †Brachythoraci Gross, 1932
                 1 Family †Homostiidae Eastman, 1907
                 2 Family †Buchanosteidae White, 1952
                 3 Family †Parabuchanosteidae Long, Mark-Kurik & Young, 2014
                 4 Family †Gemuendenaspidae Miles, 1962
                 5 †Coccosteomorphi Stensiö, 1944 - coccosteomorphs
                 6 †Pachyosteomorphi Stensiö, 1944 - pachyosteomorphs