A Bieberbach theorem for crystallographic group extensions

In this paper we prove that for each dimension $n$ there are only finitely many isomorphism classes of pairs of groups $(Γ,\mathrm{N})$ such that $Γ$ is an $n$-dimensional crystallographic group and $\mathrm{N}$ is a normal subgroup of $Γ$ such that $Γ/\mathrm{N}$ is a crystallographic group.

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