Induced Hopf Galois structures

For a finite Galois extension K/kK/k and an intermediate field F   such that Gal(K/F)Gal(K/F) has a normal complement in Gal(K/k)Gal(K/k), we construct and characterize Hopf Galois structures on K/kK/k which are induced by a pair of Hopf Galois structures on K/FK/F and F/kF/k.