Connection between $p$-adic analytic groups and linear groups

Question

I trying to prove that

a group $G$ is $p$-adic analytic if and only if is linear (as a closed subgroup of $\mathrm{GL}_n(\Bbb{Q}_p)$).

I'm not sure if the result is valid or if is necessary some additional hypothesis. If anyone knows some reference for a proof or a counterexample it would be a great help.

Answer 1

The $p$-adic metaplectic group gives a counterexample; see here. https://en.wikipedia.org/wiki/Metaplectic_group