of finite groups the embedding problem is to construct over the field k a Galois algebra L containing K as a subfield and having G as the automorphism group over k in such a way that the epimorphism of restriction of these automorphisms to K coincides with φ. It is well known (see [1], Chap. 1, § 6, Corollary 5) that if the kernel N of the embedding problem (K/k, G, φ, N) generated by the extension (1) is contained in the Frattini subgroup Φ(G) of the group G, then every solution of such a problem is necessarily a field. The purpose of the present note is to construct a series of examples of group extensions of the form (1) for which the corresponding embedding problem has only fields as solutions, but the kernel is not contained in the Frattini subgroup ofG. We note that this formulation of the problem has not yet been considered in the literature.