Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Vertebrata Lamarck, 1801 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
         Myopterygii Janvier, 1978 - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Chondrichthiomorphi see Grade Chondrichthyomorphi
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Holocephali Bonaparte, 1832
                   Superorder Holocephalimorpha Lund, 1986
                     Cochliodontomorpha
                       Order Chimaeriformes Obruchev, 1953 - chimaeras
                         Suborder Chimaeroidei Patterson, 1965 - chimaeras
                           Superfamily Callorhinchoidea Garman, 1901 [monotypic]
                             Family Callorhinchidae Garman, 1901 - plownose chimaeras
                               1 Genus †Brachymylus Smith Woodward, 1892
                               2 Genus †Ischyodus Egerton, 1843
                               3 Genus †Pachymylus Woodward, 1892
                               4 Subfamily †Edaphodontinae Owen, 1846 [monotypic]
                               5 ?Genus †Eomanodon Ward & Duffin, 1989
                               6 ?Genus †Ganodus Egerton, 1843
                               7 Genus Callorhinchus Lacepède, 1798