Space group determination: Difference between revisions

== Subgroup and supergroup relations of these space groups ==

Compiled from [https://onlinelibrary.wiley.com/doi/book/10.1107/97809553602060000001 International Tables for Crystallography (2006) Vol. A1 (Wiley)]. Simply put, for each space group, a maximum ''translationengleiche'' subgroup has lost a single type of symmetry, and a minimum ''translationengleiche'' supergroup has gained a single symmetry type. Example: P222 is a supergroup of P2, and a subgroup of P422 (and P4222 and P23). Of course the subgroup/supergroup relation is recursive, which is why P1 is also a (sub-)subgroup of P222 (but not a maximum ''translationengleiche'' subgroup). The table below does not show other types of sub/supergroup relations, e.g. non-isomorphic ''klassengleiche'' supergroups which may result e.g. from centring translations, because I find them less relevant in space group determination.

The table below is relevant because in particular twinning adds a symmetry type, and leads to an apparent space group which is the supergroup of the true space group.