[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 †Phlyctaenioidei
                 Family †Phlyctaeniidae Fowler, 1947 (1929)
                   1 Genus †Phlyctaenaspis Traquair, 1890, nom. illeg. see Genus Phlyctaenius Traquair, 1890
                   2 Genus †Monaspis Heintz, 1929, nom. illeg. see Genus Heterogaspis Strand, 1932
                   3 Genus †Jaekelaspis Heintz, 1929
                   4 Genus †Heterogaspis Strand, 1932
                   5 Genus †Phlyctaenius Traquair, 1890
                   6 Genus †Williamsaspis White, 1952
                   7 Genus †Aggeraspis Gross, 1962