The Bravais group of a reducible finite subgroup G ofis described in terms of the Bravais groups of irreducible constituent groups and connecting functions of G. A similar reduction is obtained for the centralizer of G, when no two irreducibleQ-constituents of the natural representations of G areQ-equivalent and for the normalizer of G when no twoQ-constituent groups of G areQ-equivalent. This paper can be considered as a continuation of “On Integral Groups I-III” by H Brown, J. Neubüser and H. Zassenhaus [2-4]