The subclasses Hexacorallia (anemones and "true corals") and Octocorallia (octocorals) are two reciprocally monophyletic clades that together make up the class Anthozoa (anemones, corals, and sea pens).
The subclass Hexacorallia includes six orders: Actiniaria (true sea anemones), Antipatharia (black corals), Ceriantharia (tube anemones), Corallimorpharia, Scleractinia (true or "stony" corals), and Zoanthidea.
Hexacorallia includes roughly 4,300 known extant species. As the name suggests, most hexacorallians have hexamerous symmetry (i.e., parts in multiples of 6), although eight- and ten-part symmetry are not uncommon.The most familiar group of corals, the reef builders, includes around 650 extant species (i.e., around half the known stony coral species). These are found mostly in the clear, shallow waters of the tropics.
(Daly et al. 2007 and references therein; Crowther 2011)