Decomposition of locally compact coset spaces

In a previous article by the author and P. Wesolek, it was shown that compactly generated locally compact group $G$ admits finite normal series $(G_i)$ in which factors are compact, discrete or irreducible sense no closed subgroup of lies properly between $G_{i-1}$ $G_{i}$. present article, we generalize this to an analogous decomposition coset space $G/H$ with respect subgroups, where is $H$ generated. This time, spaces $G_{i}/G_{i-1}$ $G_{i}$ there Such can be thought as generalization primitive actions groups; establish some basic properties discuss sources examples.