  We classify six-dimensional Lie groups which admit a left-invariant half-flat
SU(3)-structure and which split in a direct product of three-dimensional
factors. Moreover, a complete list of those direct products is obtained which
admit a left-invariant half-flat SU(3)-structure such that the
three-dimensional factors are orthogonal. Similar classification results are
proved for left-invariant half-flat SL(3,R)-structures on direct products with
either definite and orthogonal or isotropic factors.
