A relationship exists between factor groups of space groups and subperiodic
groups. This relationship, an isomorphism between factor groups of reducib
le space groups and subperiodic groups, can be used in the derivation of hi
gher-dimensional space groups, of lattices of space groups, and of irreduci
ble representations of space groups. Tables of the layer and rod subperiodi
c groups isomorphic to factor groups of reducible space groups are explicit
ly given. The manifestation of this relationship, in terms of the symmetry
diagrams of space groups and subperiodic groups, is also discussed.