International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2015 
International Tables for Crystallography (2015). Vol. A, ch. 1.4, pp. 4950
Section 1.4.1.6. Sequence of spacegroup types
H. Wondratschek^{e}

The sequence of spacegroup entries in the spacegroup tables follows that introduced by Schoenflies (1891) and is thus established historically. Within each geometric crystal class, Schoenflies numbered the spacegroup types in an obscure way. As early as 1919, Niggli (1919) considered this Schoenflies sequence to be unsatisfactory and suggested that another sequence might be more appropriate. Fedorov (1891) used a different sequence in order to distinguish between symmorphic, hemisymmorphic and asymmorphic space groups (cf. Section 1.3.3.3 for a detailed discussion of symmorphic space groups).
The basis of the Schoenflies symbols and thus of the Schoenflies listing is the geometric crystal class. For the present spacegroup tables, a sequence might have been preferred in which, in addition, spacegroup types belonging to the same arithmetic crystal class were grouped together. It was decided, however, that the longestablished sequence in the earlier editions of International Tables should not be changed.
In Table 1.4.1.3, those geometric crystal classes are listed in which the Schoenflies sequence separates space groups belonging to the same arithmetic crystal class (cf. Section 1.3.4.4 for the definition and discussion of arithmetic crystal classes). The space groups are rearranged in such a way that space groups of the same arithmetic crystal class are grouped together. The arithmetic crystal classes are separated by rules spanning the last three columns of the table and the geometric crystal classes are separated by rules spanning the full width of the table. In all cases not listed in Table 1.4.1.3, the Schoenflies sequence, as used in the spacegroup tables, does not break up arithmetic crystal classes. Nevertheless, some rearrangement would be desirable in other arithmetic crystal classes too. For example, the symmorphic space group should always be the first entry of each arithmetic crystal class.

References
Fedorov, E. S. (1891). The symmetry of regular systems of figures. (In Russian.) [English translation by D. & K. Harker (1971). Symmetry of crystals, pp. 50–131. American Crystallographic Association, Monograph No. 7.]Niggli, P. (1919). Geometrische Kristallographie des Diskontinuums. Leipzig: Borntraeger. [Reprint (1973). Wiesbaden: Sändig.]
Schoenflies, A. (1891). Krystallsysteme und Krystallstruktur. Leipzig: B. G. Teubner. [Reprint (1984). Berlin: SpringerVerlag.]