I am interested in finitely generated groups $G$ that are residually finite and have the following property: For each $d \geq 1$, $G$ has subgroups of finite index $d$, and all such subgroups are isomorphic.

I know three infinite families of such groups: (1) Free abelian groups $\mathbb Z^n$ (2) Free groups $F_n$ (3) Fundamental groups of closed orientable surfaces $\Gamma_n = \pi_1 (\Sigma_n)$.

The way to see that these are indeed examples is via topology: the classifying spaces of these groups are tori, graphs and surfaces and we understand their covering theory.

[Note: some geometric group theorist claim that these are the easiest torsion-free groups that exist. Their outer automorphism groups are given by $GL_n(\mathbb Z)$, $Out(F_n)$ and $Mod^{\pm}_n$, groups that generated a vast body of research.]

**Are there more (than the above mentioned) examples of such groups?**

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