32 Point groups and their relations m3m Class Group names 43m432m3 6/mmm Cubic 23 m3 432 43m m3m 4/mmm 23 6mm6m26226/m3m Hexagonal 6 6 % 622 6mm 62m 42m 4mm 422 4/m mmm Trigonal 3 3 32 3m 3m 3m 32 Tetragonal 422 Amm 42m mm2 222 2/m Monoclinic 2 头 222 mm2 nunm Orthorhombic Subgroup relations of the 32 crystallographic point groups Triclinic y (rows represent group orders from bottom to top as: 1,2,3,4,6,8,12,16,24,and48.) 2,3,6:2-fold,3-fold,6-fold rotation symmetry m:mirror symmetry 6 4-bar,6-bar:4-fold,6-fold retoinversion6 32 Point groups and their relations 2, 3, 6: 2-fold, 3-fold, 6-fold rotation symmetry m: mirror symmetry 4-bar, 6-bar: 4-fold, 6-fold retoinversion