Finite partition of a group by left cosets of subgroups

Let $G$ be a group.
Suppose there exist a finite sequence of elements $a_1, \cdots, a_n$ and a finite sequence of subgroups $H_1, \cdots, H_n$ such that $G = \bigcup_{i=1}^n a_iH_i$ is a disjoint union.
If $(G: H_1) = \cdots = (G : H_n) \lt \infty$, then $H_1= \cdots = H_n?$

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Explicit construction of Haar measure on a profinite group

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