  In this paper we consider the problem of classifying the isomorphism classes
of extensions of degree pk of a p-adic field, restricting to the case of
extensions without intermediate fields. We establish a correspondence between
the isomorphism classes of these extensions and some Kummer extensions of a
suitable field F containing K. We then describe such classes in terms of the
representations of Gal(F/K). Finally, for k = 2 and for each possible Galois
group G, we count the number of isomorphism classes of the extensions whose
normal closure has a Galois group isomorphic to G. As a byproduct, we get the
total number of isomorphism classes.
