  The orbifold group of the Borromean rings with singular angle 90 degrees,
$U$, is a universal group, because every closed oriented 3--manifold $M^{3}$
occurs as a quotient space $M^{3} = H^{3}/G$, where $G$ is a finite index
subgroup of $U$. Therefore, an interesting, but quite difficult problem, is to
classify the finite index subgroups of the universal group $U$. One of the
purposes of this paper is to begin this classification. In particular we
analyze the classification of the finite index subgroups of $U$ that are
generated by rotations.
