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Let $G$ be a finite group and use Cayley's theorem to embed $G$ into the symmetric group $S_n$. Is it possible via Sage to get the subposet of the strong Bruhat order (or the weak Bruhat order) on $S_n$ that has the points of $G$ inside $S_n$ with the induced poset structure?

Let $G$ be a finite group and use Cayley's theorem to embed $G$ into the symmetric group $S_n$. Is it possible via Sage to get the subposet of the strong Bruhat order (or the weak Bruhat order) on $S_n$ that has the points of $G$ inside $S_n$ with the induced poset structure?