Teichertoceras is a discosorid

Discosorida

Discosorida is a unique order of cephalopods that lived from the beginning of the Middle Ordovician, through the Silurian, and into the Devonian. Discosorids are unique in the structure and formation of the siphuncle, the tube that runs through and connects the chambers in cephalopods, which unlike...

 genus in the family Westonoceratidae

Westonoceratidae

Westonoceratidae are exogastric, mostly compressed, Discosorida of moderate size from the Middle Ordovician to the Lower Silurian.The siphuncle is typically close to the convexly curved outer margin of the phragmocone -the chambered part of the shell- taken to be ventral but may be more central in...

 characterized by an endogastric curvature to the early portion of the phragmocone.

The shell of Teichertoceras is moderately compressed; the early portion a narrow expanding cyrtocone that in the adult become more swollen, taking on an exogastric aspect. The body chamber in the adult is contracted toward the aperture. The siphuncle

Siphuncle

The siphuncle is a strand of tissue passing longitudinally through the shell of a cephalopod mollusk. Only cephalopods with chambered shells have siphuncles, such as the extinct ammonites and belemnites, and the living nautiluses, cuttlefish, and Spirula...

 is ventral. Bullettes at the adapical ends of the connecting rings are small.

Teichertoceras is thought to have given rise to Westonoceras

Westonoceras

Westonoceras is an extinct nautiloid genus from the Discosorida that lived during the Middle and Late Ordovician that has been found in North America, Greenland, and Northern Europe...

and Faberoceras

Faberoceras

Faberoceras is an extinct genus of prehistoric nautiloid. The nautiloids are a subclass of shelled cephalopods that were once diverse and numerous but are now represented by only a handful of species.-References:...

and to be derived from Ulrichoceras

Ulrichoceras

Ulrichoceras is recognised as the basal cyrtogomphoceratid genus, which is the source for the rest of the Cyrtogomphoceratidae as well as for the Westonoceratidae...

. It is found in the Middle Ordovician of North America.