Nearly parallel G_2-structures with large symmetry group

We prove the existence of a one-parameter family of nearly parallel G_2-structures on the manifold S^3x R^4, which are mutually non-isomorphic and invariant under the cohomogeneity one action of the group SU(2)^3. This family connects the two locally homogeneous nearly parallel G_2-structures which are induced by the homogeneous ones on the sphere S^7.