Chapter 2.5 Graphs for klassengleiche subgroups

Symmetry relations between space groups

First Online Edition (2006)

Part 2. Maximal subgroups of the plane groups and space groups

  1. Volker Gramlich1,
  2. Hans Wondratschek2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000546

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Gramlich, V. and Wondratschek, H. 2006. Graphs for klassengleiche subgroups. International Tables for Crystallography. A1:2:2.5:415–425.

Author Information

  1. 1

    Laboratorium für Kristallographie, Eidgenössische Technische Hochschule, Wolfgang-Pauli Strasse 10, ETH Hönggerberg HCI, CH-8093 Zürich, Switzerland

  2. 2

    Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany

Publication History

  1. Published Online: 1 JAN 2006


This chapter presents 29 contracted graphs for the maximal klassengleiche subgroups of the space groups of the 32 crystal classes. The graphs for crystal classes 1, equation image and equation image are not included, because in these classes there is only one space-group type and their diagrams would be trivial. Isomorphic subgroups are not indicated, because each space group has an infinite number of them. In case of mutual group–subgroup relations, e.g.equation imageequation image or equation imageequation image, group and subgroup are connected by horizontal arrows which point from the group to the subgroup.


  • graphs of group–subgroup relations;
  • subgroup graphs;
  • klassengleiche subgroups;
  • maximal subgroups