[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
         Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
           Subclass Holocephali Bonaparte, 1832
             Superorder Holocephalimorpha Lund, 1986
               Cochliodontomorpha
                 Order †Chondrenchelyiformes Moy-Thomas, 1939 [monotypic]
                   Family †Chondrenchelyidae Jordan, 1923
                     1 Genus †Chondrenchelys Traquair, 1888