# Every group of totally disconnected type is locally profinite?

Let $$G$$ be a Hausdorff topological group in which every point has a neighborhood basis of open compact neighborhoods. Let's call this a group of totally disconnected (td)-type.

On the other hand, we have a notion of a locally profinite group, a Hausdorff topological group which has a neighborhood basis of the identity consisting of open compact subgroups. A locally profinite group is obviously of td-tytpe.

Is there an example of a group of td-type which is not locally profinite?