In a previous article of Wesolek and the author, it was shown that a compactly generated locally compact group πΊ admits a finite normal series (πΊπ) in which the factors are compact, discrete or irreducible in the sense that no closed normal subgroup of πΊ lies properly between πΊπβ1 and πΊπ. In the present article, we generalize this series to an analogous decomposition of the coset space πΊβπ» with respect to closed subgroups, where πΊ is locally compact and π» is compactly generated. This time, the irreducible factors are coset spaces πΊπβπΊπβ1 where πΊπ is compactly generated and there is no closed subgroup properly between πΊπβ1 and πΊπ. Such irreducible coset spaces can be thought of as a generalization of primitive actions of compactly generated locally compact groups; we establish some basic properties and discuss some sources of examples.