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Let K be a totally real multi-quadratic fields and let $\mathcal{O}$ be its ring of integers. I would like to compute the orders of the finite subgroups of the discrete group $\mathrm{SL}_{2}(\mathcal{O})$. These orders are helpful for computing Euler characteristics.

I would like to know whether there is any methods to do the computations and where to find them. Thanks for all.

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    $\begingroup$ the finite subgroups are all abelian $\endgroup$
    – Venkataramana
    Commented Dec 25, 2019 at 13:59

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