[Phylum] Chordata Bateson, 1885 - chordates
   Subphylum Craniata auct.
     Infraphylum Vertebrata Lamarck, 1801 - vertebrates
       Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
         Class Osteichthyes Huxley, 1880 - bony fishes and tetrapods see Clade Osteichthyes Huxley 1880 [Moore & Near 2020]
           Subclass Sarcopterygii Romer, 1955 - lobe-finned fishes and tetrapods see [unranked] Sarcopterygii Romer, 1955
             Infraclass Dipnomorpha Ahlberg, 1991 see [unranked] Dipnomorpha Ahlberg, 1991
               Superorder Dipnoi Müller, 1844 see Class Dipneusti
                 Order †Dipteriformes
                   Family †Chirodipteridae Campbell & Barwick, 1990
                     1 Genus †Chirodipterus Jaekel, 1933
                     2 Subfamily †Pillararhynchinae Long, 1992
                     3 Subfamily †Conchodontinae Krupina, 2004