The Collaborative International Dictionary of English v.0.48:

Tetrabranchiata \Tet`ra*bran`chi*a"ta\, n. pl. [NL. See
   Tetra-, and Branchia.] (Zool.)
   An order of Cephalopoda having four gills. Among living
   species it includes only the pearly nautilus. Numerous genera
   and species are found in the fossil state, such as Ammonites,
   Baculites, Orthoceras, etc.
   [1913 Webster]