Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Infraphylum Vertebrata Lamarck, 1801 - vertebrates
         Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
           Grade †Placodermiomorphi [monotypic]
             Class †Placodermi McCoy, 1848 [paraphyletic?]
               Order †Arthrodiriformes Grande & Eastman, 1986 - arthrodires see [unranked] Arthrodira Woodward, 1891
                 Suborder †Phlyctaenioidei
                   Family †Phlyctaeniidae Fowler, 1947 (1929)