Small order of corals, known only from Carboniferous rocks in Europe and Asia, and represented by two genera, Hexophyllia and Heterophyllia. It is included in the Zoantharia because its members possess septa, and because of the microstructure of the calcareous skeleton. The septa are arranged differently from those in other orders. The four original septa are conjoined axially, and new septa are formed attached to these at their axial ends.