The order is divided into three families.
Fam. 1. Monoprionidae.—Cups arranged uniserially on one side of the axis.
The principal genera are Monograptus, with the axis straight, curved, or helicoid, from many horizons in the Silurian strata; Rastrites, with a spirally coiled axis, Silurian; Didymograptus, Ordovician; and Coenograptus, Ordovician.
Fam. 2. Diprionidae.—Cups arranged in two or four vertical rows on the axis.
Diplograptus, Ordovician and Silurian; Climacograptus, Ordovician and Silurian; and Phyllograptus, in which the axis and cups are arranged in such a manner that they resemble an ovate leaf.
Fam. 3. Retiolitidae.—Cups arranged biserially on a reticulate axis.
Retiolites, Ordovician and Silurian; Stomatograptus, Retiograptus, and Glossograptus, Ordovician.
Fossil Corals possibly allied to Hydrozoa.
Among the many fossil corals that are usually classified with the Hydrozoa the genus Porosphaera is of interest as it is often supposed to be related to Millepora. It consists of globular masses about 10-20 mm. in diameter occurring in the Upper Cretaceous strata. In the centre there is usually a foreign body around which the coral was formed by concentric encrusting growth. Running radially from pores on the surface to the centre, there are numerous tubules which have a certain general resemblance to the pore-tubes of Millepora. The monomorphic character of these tubes, their very minute size, the absence of ampullae, and the general texture of the corallum, are characters which separate this fossil very distinctly from any recent Hydroid corals. Porosphaera, therefore, was probably not a Hydrozoon, and certainly not related to the recent Millepora.
Closely related to Porosphaera apparently are other globular, ellipsoidal, or fusiform corals from various strata, such as Loftusia from the Eocene of Persia, Parkeria from the Cambridge Greensand, and Heterastridium from the Alpine Trias. In the last named there is apparently a dimorphism of the radial tubes.