  Semi-direct products of finite groups have permutation representations that
are constructed from the permutation representations of their constituents. One
can envision these in a metaphoric sense in which a rope is made from a bundle
of threads. In this way, subgroups and quotients are easily visualized. The
general idea is applied to the finite subgroups of the special unitary group of
$(2\times 2)$-matrices. Amusing diagrams are developed that describe the unit
quaternions, the binary tetrahedral, octahedral, and icosahedral group as well
as the dicyclic groups. In all cases, the quotients as subgroups of the
permutation group are readily apparent. These permutation representations lead
to injective homomorphisms into semi-direct products.
