Aston Martin’s IPO will provide further clues to which category ultra-expensive carmakers really belong.

its context:economist

Grammatically,you need to have " clues to which..." and " to which... belong ". So is "to" double duty here？

Or it should have been:

Aston Martin’s IPO will provide further clues to which category ultra-expensive carmakers really belong to.

Do you think it is acceptable or the writer made a mistake?