  We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form
is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds
that admit an invariant closed 4-form with stabiliser Sp(2)Sp(1). Our
constructions entail the notion of SO(4)-structures on 7-manifolds. We present
a thorough investigation of the intrinsic torsion of such structures, leading
to the construction of explicit Lie group examples with invariant intrinsic
torsion.
