  Let K be a number field, let A be a finite dimensional semisimple K-algebra
and let Lambda be an O_K-order in A. It was shown in previous work that, under
certain hypotheses on A, there exists an algorithm that for a given (left)
Lambda-lattice X either computes a free basis of X over Lambda or shows that X
is not free over Lambda. In the present article, we generalise this by showing
that, under weaker hypotheses on A, there exists an algorithm that for two
given Lambda-lattices X and Y either computes an isomorphism X -> Y or
determines that X and Y are not isomorphic. The algorithm is implemented in
Magma for A=Q[G], Lambda=Z[G] and Lambda-lattices X and Y contained in Q[G],
where G is a finite group satisfying certain hypotheses. This is used to
investigate the Galois module structure of rings of integers and ambiguous
ideals of tamely ramified Galois extensions of Q with Galois group isomorphic
to Q_8 x C_2, the direct product of the quaternion group of order 8 and the
cyclic group of order 2.
