The twin operation belongs to to the point group of the lattice but not to the point group of the crystal. Therefore, the point group of the crystal must be a subgroup of the point group of the lattice, i.e. the crystal shows only a part (merohedry) of the symmetry elements belonging to the its lattice which, instead, shows holohedry (complete symmetry). The twinning element of symmetry may (Class I of twins by merohedry) or may not belong to the Laue class of the crystal (Class II of twins by merohedry): Examples - Class I: in crystals with point group 2 (Laue group 2/m) the mirror plane m acts as twinning operator . Class II: in crystals with point group 4 (Laue group 4/m) a mirror plane m parallel to the foufold axis 4 acts as twinning operator.
Chapter 3.3 of International Tables of Crystallography, Volume D