An order of the cnidarian subclass Alcyonaria (Octocorallia). The Coenothecalia have no spicules but form colonies with a massive skeleton composed of fibrocrystalline argonite fused into lamellae. The skeleton is perforated by both numerous wide cylindrical cavities occupied by the polyps, and narrow ones containing the solenial systems. In the calyx of the polyp, septalike structures of stony coral, or pseudosepta, are formed. The order includes a few genera, of which Heliopora, or the blue coral, is often found on coral reefs.