International
Tables for Crystallography Volume A Spacegroup symmetry Edited by Th. Hahn © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. A, ch. 4.3, pp. 7576

In the synoptic tables of IT (1935) and IT (1952), for cubic space groups short and full Hermann–Mauguin symbols were listed. They agree, except that in IT (1935) the tertiary symmetry element of the space groups of class 432 was omitted; it was reestablished in IT (1952).
In the present edition, the symbols of IT (1952) are retained, with one exception. In the space groups of crystal classes and , the short symbols contain instead of 3 (cf. Section 2.2.4 ). In Table 4.3.2.1, short and full symbols for all cubic space groups are given. In addition, for centred groups F and I and for P groups with tertiary symmetry elements, extended spacegroup symbols are listed. In space groups of classes 432 and , the product rule (as defined below) is applied in the first line of the extended symbol.
Conventionally, the representative directions of the primary, secondary and tertiary symmetry elements are chosen as [001], [111], and [] (cf. Table 2.2.4.1 for the equivalent directions). As in tetragonal and hexagonal space groups, tertiary symmetry elements are not independent. In classes 432, and , there are product rules where the tertiary symmetry element is in parentheses; analogous rules hold for the space groups belonging to these classes. When the symmetry directions of the primary and secondary symmetry elements are chosen along [001] and [111], respectively, the tertiary symmetry direction is [011], according to the product rule. In order to have the tertiary symmetry direction along [], one has to choose the somewhat awkward primary and secondary symmetry directions [010] and [].
Examples
Owing to periodicity, the tertiary symmetry elements alternate; diagonal axes 2 alternate with parallel screw axes ; diagonal planes m alternate with parallel glide planes g; diagonal n planes, i.e. planes with glide components , alternate with glide planes a, b or c (cf. Chapter 4.1 and Tables 4.1.2.2 and 4.1.2.3 ). For the meaning of the various glide planes g, see Section 11.1.2 and the entries Symmetry operations in Part 7 .
The extended symbol of (202) shows clearly that , , and are maximal subgroups. , , and are maximal subgroups of (229). Space groups with d glide planes have no k subgroup of lattice P.

References
Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). 1. Band, edited by C. Hermann. Berlin: Borntraeger. [Revised edition: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]International Tables for Crystallography (1995). Vol. A, fourth, revised ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT (1995).]
International Tables for Xray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Abbreviated as IT (1952).]