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I have modified an incorrect statement which suggested chiral groups would be the same as Sohncke groups. This is untrue. Sohncke groups contain only operations of the first kind and thus chiral crystal structures do form in Sohncke groups. On the other hand, chiral group means that the group itself - not just the structure crystallizing in it - is chiral. For that, it is necessary that the Euclidean nornalizer of the group contains only operations of the first kind, which is a much stronger condition. Accordingly, there are 65 Sohncke groups and 22 chiral groups (in 3D). All chiral groups are Sohncke groups, but the opposite in not true.
See also the online dictionary of crystallography about Sohncke groups and chiral groups.
