  We show that all spin groups of non-definite, quinary quadratic forms over a
field with characteristic 0 can be represented as 2 by 2 matrices with entries
in an associated quaternion algebra. Over local and global fields, we further
study maximal arithmetic subgroups of such groups, and show that examples can
be produced by studying orders of the quaternion algebra. In both cases, we
relate the algebraic properties of the underlying rings to sufficient and
necessary conditions for the groups to be isomorphic and/or conjugate to one
another.
