Extensions with Galois group 2 + S 4 ∗ D 8 in characteristic 3

For K a field of characteristic 3 we give explicitly the whole family of Galois extensions of K with Galois group 2 + S 4 ∗ D 8 and determine the discriminant of such an extension. In the case when K is the field of fractions of a formal power series ring in 3 variables, this result is interesting in the context of Abhyankar's Normal Crossings Local Conjecture.