Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct. see Subphylum Vertebrata Cuvier, 1812
       Vertebrata (Lamarck, 1801) - vertebrates see Subphylum Vertebrata Cuvier, 1812
         Myopterygii - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Chondrichthiomorphi
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Holocephali Bonaparte, 1832
                   Superorder †Paraselachimorpha (Lund, 1977)
                     ?Order †Petalodontiformes Zangerl, 1981
                       Family †Petalodontidae Newberry & Worthen, 1866
                         Genus †Polyrhizodus McCoy, 1848