The Early Carnian (Upper Triassic) phaceloid coral originally described by Volz (1896) as Hexastraea fritschi, type species of QuenstedtiphylliaMelnikova, 1975, reproduced asexually by “Taschenknospung” (pocket-budding), a process documented herein for the first time. This type of budding is recognized only in the Amphiastraeidae, a family thus far recorded only from Jurassic-Cretaceous strata. Similar to amphiastraeids, Quenstedtiphyllia fritschi (Volz, 1896) has separate septal calcification centers and a mid-septal zone built of serially arranged trabeculae. The most important discriminating characters of the new amphiastraeid subfamily Quenstedtiphylliinae are one-zonalendotheca and radial symmetry of the corallite in the adult stage (in contrast to two-zonal and bilateral symmetry in the adult stage in Amphiastraeinae). Quenstedtiphyllia fritschi shares several primitive skeletal characters (plesiomorphies) with representatives of Triassic Zardinophyllidae and, possibly, Paleozoic plerophylline rugosans: e.g., thick epithecal wall and strongly bilateral early blastogenetic stages with the earliest corallite having one axial initial septum. To interpret the phylogenetic status of amphiastraeid corals, we performed two analyses using plerophylline rugosans and the solitary scleractinian Protoheterastraea, respectively, as the outgroups. The resulting phylogenetic hypotheses support grouping the Zardinophyllidae with the Amphiastraeidae in the clade Pachythecaliina (synapomorphy: presence of pachytheca). Taschenknospung is considered an autapomorphy for the Amphiastraeidae. This study is the first attempt to analyze the relationships of the Triassic corals cladistically.