Mitchell Trott has report a bug in 'SubdirectProduct'. The projection
returned by 'Projection' doesn't work correctly, the preimages might
not lie in the subdirect product.
The projections work correctly if the arguments are perm groups or ag
groups *not* created as subdirect product, for example, if the
arguments are groups created using 'Group' and subgroups of such
groups. However, if you iterate this process, i.e., form the
subdirect product of one or two subdirect products, the projections
will show this incorrect behaviour.
A fix is available from "Gap-Trouble@Math.RWTH-Aachen.DE".