Data structure for efficient group lookup

I need a data structure, which allows efficient queries for ‘give me the group of x‘.

Let me give you an example:

Group 1: [a, b, c]  Group 2: [d, e] Group 3: [f]  getGroupOf(d) -> [d, e] 

There are no significant constraints on storage or construction time. I only need getGroupOf to be O(logn) or faster.

I am thinking about using a Dictionary<Element, Set<Element>> where entries for all elements in a group share the same set reference. This would make lookup effectively O(1) or O(logn) depending on the dictionary implementation, but would result in a lot of entries.

This feels fairly bloated, and I am wondering: is there is a more elegant data structure to accomplish this?