Bourne, 1900
Families: The order contains 18 families.
Family Acroporidae
Family Agariciidae
Family Astrocoeniidae
Family Caryophylliidae
Family Dendrophyllidae
Family Euphylliidae
Family Faviidae
Family Flabellidae
Family Fungiidae
Family Merulinidae
Family Mussidae
Family Oculinidae
Family Pectiniidae
Family Pocilloporidae
Family Poritidae
Family Siderastreidae
Family Trachyphylliidae
Descriptiom: Colonies with calcareous sketeton and polyps with tentacles arranged in sixes.