Phylum Chordata Bateson, 1885 - chordates
   Subphylum Vertebrata Cuvier, 1812 - vertebrates
     Pisces
       Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
         Subclass Holocephali Bonaparte, 1832
           Order Chimaeriformes Obruchev, 1953 - chimaeras
             Family Callorhynchidae Garman, 1901 see Family Callorhinchidae Garman, 1901
             Family Chimaeridae Rafinesque, 1815 - shortnose chimaeras
             Family †Cochliodontidae Owen, 1867
             Family †Echinochimaeridae
             Family †Menaspidae Woodward, 1891
             Family Rhinochimaeridae Garman, 1901 - longnose chimaeras
             Family †Squalorajidae Woodward, 1886