This article is a taxonomic study of all spongy radiolarian taxa with five to six coplanar and four tetrahedrally disposed spines or spongy arms occurring in the middle Carnian from the Koseyahya section, near the town of Elbistan, SE Turkey. This fauna is characteristic of the Tetraporobrachia haeckeli radiolarian Zone, and comes from an 8 m thick succession of clayey-cherty limestones occurring at the lower part of the section. In addition, a few species from the Middle and Upper Triassic from other areas have been also included in this study to improve some generic diagnoses and to better understand the diversity and evolutionary trends of some genera, subfamilies and families. The taxonomy at the generic and suprageneric levels is based primarily on the types of microsphere. This new approach allowed new taxonomic arrangements of genera and suprageneric units, and suggested new and unexpected phylogenetic relationships among these radiolarians and between them and younger radiolarians. The authors discuss and describe 42 species, of which 36 are new, and 12 genera of which three are new (Charlottalum, Pentaspongodisculus, and Trimiducaella). The genera Pseudohagiastrum Pessagno, Natraglia Pessagno, Cantalum Pessagno and others are reinterpreted. All the genera studied, except Charlottalum, are assigned to three subfamilies, of which two (Pseudohagiastrinae and Trimiducinae) are new, and to two families (Angulobracchiidae and Relindellidae). The genus Charlottalum is described to replace the genus Cantalum, which has been erroneously used until present for Late Triassic pantanelliids with four tetrahedrally disposed three-bladed spines.