Point group 32 is obviously a merging of two different groups 321 and 312 since for both setups space groups exist which cannot be transferred into each other. For the first the basis vector a is parallel to the two-fold rotation whereas for 312 both directions are 30 degrees rotated to each other, i.e. for 312 the twofold rotation axis is parallel to . This does not automatically enable a subgroup transition. Nevertheless, the International Tables list a transition for P312 described by P112 (in contrast to P321 where P121 is given). Why are the subgroups distinguished in this way, although the crystallographic direction of 2 given in P312 is not the same as in P112?