Summary: In a previous paper, the second author established that, given finite fields \(F < E\) and certain subgroups \(C\leq E^\times\), there is a Galois connection between the intermediate field lattice \(\{L \mid F \leq L \leq E\}\) and \(C\)’s subgroup lattice. Based on the Galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product \(C\rtimes\mathrm{Gal}(E/F)\). However, the analysis when \(|F|\) is a Mersenne prime is more complicated, so certain cases were omitted from that paper. The present exposition, which is a reworking of the previous article, provides a uniform analysis over all the families, including the previously undetermined ones. In the group \(C\rtimes \mathrm{Gal}(E/F)\), we use the Galois connection to calculate stabilizers of linear characters, and these stabilizers determine the full character degree set. This is shown for each subgroup \(C\leq E^\times\) which satisfies the condition that every prime dividing \(|E^\times :C|\) divides \(|F^\times|\).