Lyrogoniatitites is a neoglyphiocercean

Neoglyphiocerataceae

Neoglyphiocerataceae is one of seventeen superfamilies of the Goniatitina suborder. They are an extinct group of ammonoid, which are shelled cephalopods related to squids, belemnites, octopodes, and cuttlefish, and more distantly to the nautiloids....

 ammonite, in the order Goniatitida, related to genera like Alaoceras

Alaoceras

Alaoceras is an ammonoid cephalopod from the upper Paleozoic included in the goniatitid family Cravenoceratidae, named by Ruzhentsev & Bogoslovskaya in 1971....

, Cravenoceras

Cravenoceras

Cravevoceras is an Upper Paleozoic ammonite in the gonititid family Cravenoceratidae, probably derived from Pachylyroceras and contemporaty with other cravenoceratid genera like Caenolyroceras, Tympanoceras and later Alaoceras and Lyrogoniatites...

, Dumbarigloria and Pachylyroceras

Pachylyroceras

Pachylyroceras is a large, generally subglobular, Upper Mississippian gonitite and included in the cephalopod subclass Ammonoidea.-Recognition:...

.

Description

Lyrogoniatites is similar to Neoglyphioceras, but with broader shell and a smaller number (30-60) of longitudinal lirae and with a ventral (hyponomic) sinus and ventrolateral salients (projections) in all growth stages. As with Neoglyphioceras the ventral lobe is rather narrow.

Taxonomic relations

W.M. Furnish, et al, 2009, in the revised Treatise

Treatise on Invertebrate Paleontology

The Treatise on Invertebrate Paleontology published by the Geological Society of America and the University of Kansas Press, is a definitive multi-authored work of some 50 volumes, written by more than 300 paleontologists, and covering every phylum, class, order, family, and genus of fossil and...

 includes Lyrogoniatites in the neoglyphioceratid subfamily, Lyrogoniatitinae

Lyrogoniatitinae

Lyrogoniatitinae is one of two subfamilies of the Cravenoceratidae family. They are an extinct group of ammonoid, which are shelled cephalopods related to squids, belemnites, octopuses, and cuttlefish, and more distantly to the nautiloids.-References:...

, along with Alaoceras, Caenolyroceras, Dombarigloria, and Pachylyroceras. D. Korn (2006) on the other hand put Lyrogoniatites in the neoglyphioceratacean family Cravenoceratidae

Cravenoceratidae

The Cravenoceratidae is one of six families included in the ammonoid superfamily Neoglyphiocerataceae, which lived during the latter part of the Paleozoic era....

 instead, and in the subfamily Lyrogoniatitinae along with such as Caenolyroceras and Pachylyroceras. Others, (e.g. GONIAT) also include Lyrogoniatites in the Cravenoceratidae but in the Cravenoceratinae.

The older Treatise (Miller, Furnish, and Schindiwold 1957) puts Lyrogoniatites along with Neoglyphioceras in the Goniatitidae

Goniatitidae

Goniatitidae is one of three families of the Goniatitaceae superfamilies. They are an extinct group of ammonoid, which are shelled cephalopods related to squids, belemnites, octopuses, and cuttlefish, and more distantly to the nautiloids.-References:...

 and subfamily Neoglyphioceratinae, differentiating the two on the basis of the umbilicus -- that of Lyrogoniatites being moderately large, that of Neoglyphioceras being narrow.

References

• GONIAT online
• W.M. Furnish, et al, 2009, Treatise on Invertebrate Paleontology, Part L (Revised) Vol 2. Paleozoic Ammonoidea ... http://paleodb.org/cgi-bin/bridge.pl?action=basicTaxonInfo&taxon_no=13767
• D. Korn, 2006. Paleozoic ammonoid classification. http://paleodb.org/cgi-bin/bridge.pl?a=displayReference&reference_no=18963
• Miller, Furnish, and Schindewolf, 1957. Treatise on Invertebrate Paleontology, Part L, Ammonoidea.
• Saunders, Work, and Nikolaeva, 1999. Evolution of Complexity in Paleozoic Ammonoid Sutures, Supplementary Material. http://www.sciencemag.org/site/feature/data/1043099.xhtml