If the non-translational symmetry operations (center of symmetry, rotation axes, mirror planes and rotary inversion axes) are considered, there are 32 unique point groups that can be defined. Point groups were first used by crystallographers to describe the external shapes of crystals. For example, the crystal shown here is monoclinic point group 2/m because the various crystal faces are related by a 2-fold rotation axis, a mirror plane (perpendicular to the rotation axis) and a center of symmetry.
The symmetry of an X-ray photo is the point group symmetry plus a center of symmetry (if one is not already present). These Laue symmetries and the point groups from which they are derived are displayed in the table below: