  We consider a short exact sequence $1\to H\to G\to K\to 1$ of Polish groups
and consider what can be deduced about the dynamics of $G$ given information
about the dynamics of $H$ and $K$. We prove that if the respective universal
minimal flows $M(H)$ and $M(K)$ are metrizable, then so is $M(G)$. Furthermore,
we show that if $M(H)$ and $M(K)$ are metrizable and both $H$ and $K$ are
uniquely ergodic, then so is $G$. We then discuss several examples of these
phenomena
