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. 6871

The synoptic table of IT (1935) contained spacegroup symbols for the six orthorhombic `settings', corresponding to the six permutations of the basis vectors a, b, c. In IT (1952), lefthanded systems like were changed to righthanded systems by reversing the orientation of the c axis, as in . Note that reversal of two axes does not change the handedness of a coordinate system, so that the settings , , and are equivalent in this respect. The tabulation thus deals with the possible righthanded settings. For further details see Section 2.2.6.4.
An important innovation of IT (1952) was the introduction of extended symbols for the centred groups A, B, C, I, F. These symbols are systematically developed in Table 4.3.2.1. Settings which permute the two axes a and b are listed side by side so that the two C settings appear together, followed by the two A and the two B settings.
In crystal classes mm2 and 222, the last symmetry element is the product of the first two and thus is not independent. It was omitted in the short Hermann–Mauguin symbols of IT (1935) for all space groups of class mm2, but was restored in IT (1952). In space groups of class 222, the last symmetry element cannot be omitted (see examples below).
For the new `double' glide plane symbol `e', see the Foreword to the Fourth Edition (IT 1995) and Section 1.3.2, Note (x) .
The present section emphasizes the use of the extended and full symbols for the derivation of maximal subgroups of types I and IIa; maximal orthorhombic subgroups of types IIb and IIc cannot be recognized by inspection of the synoptic Table 4.3.2.1.

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).]
Bertaut, E. F. (1976). Study of principal subgroups and of their general positions in C and I groups of class mmm–D_{zh}. Acta Cryst. A32, 380–387.