Cocalibrated G(2)-structures are structures naturally induced on hypersurfaces in Spin(7)-manifolds. Conversely, one may start with a seven-dimensional manifold M endowed with a cocalibrated G(2)-structure and construct via the Hitchin flow a Spin(7)-manifold which contains M as a hypersurface. In this article, we consider left-invariant cocalibrated G(2)-structures on Lie groups G which are a direct product G = G(4) X G(3) of a four-dimensional Lie group G(4) and a three-dimensional Lie group G(3). We achieve a full classification of the Lie groups G = G(4) X G(3) which admit a left-invariant cocalibrated G(2)-structure. (C) 2013 Elsevier B.V. All rights reserved.