### ...- semigroups.

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Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal{P}$ of group compactifications, one can ask whether there exist compactifications ${N}^{\text{'}}$ and ${K}^{\text{'}}$ of $N$ and $K$ such that the universal $\mathcal{P}$-compactification of $G$ is canonically isomorphic to an extension of ${N}^{\text{'}}$ by ${K}^{\text{'}}$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal{P}$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.