Derivation of subgroup network of three-dimensional crystallographic symmetry group
三维空间子群网的推导

The subgroup network of the three-dimensional crystallographic symmetry group has been derived based on the two maximal finite groups corresponding to two geometrically inequivalent classes. First, the geometrical meaning of every group element of these two maximal finite groups was analysed, then all the subgroups of them was derived according to the relationship between supergroup and subgroup. The advantages of algebraic crystallography based on quadratic form theory were discussed.