  Classical Clifford theory studies the decomposition of simple $G$-modules
into simple $H$-modules for some normal subgroup $H \triangleleft G$. In this
paper we deal with chains of normal subgroups $1 \triangleleft G_1
\triangleleft \cdots \triangleleft G_d =G$, which allow to consider fragments
and in particular glider representations. These are given by a descending chain
of vector spaces over some field $K$ and relate different representations of
the groups appearing in the chain. Picking some normal subgroup $H
\triangleleft G$ one obtains a normal subchain and one can construct an induced
fragment structure. Moreover, a notion of irreducibility of fragments is
introduced, which completes the list of ingredients to perform a Clifford
theory.
