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?]
               1 Order †Pseudopetalichthyiformes [monotypic]
               2 Order †Acanthothoraciformes see Order Acanthothoraci Stensiö, 1944
               3 Order †Rhenaniformes [monotypic] see Order Rhenanida Broili, 1930
               4 Order †Antiarchiformes Grande & Eastman, 1986 - antiarchs see [unranked] Antiarchi Cope, 1885
               5 Order †Petalichthyiformes see Order Macropetalichthyiformes
               6 Order †Ptyctodontiformes [monotypic]
               7 Order †Arthrodiriformes Grande & Eastman, 1986 - arthrodires see [unranked] Arthrodira Woodward, 1891