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Nonuniqueness of semidirect decompositions of groups is an insufficientlystudied question in contrast to direct decompositions. We obtain some resultsabout semidirect decompositions for semidirect products with factors which arenontrivial direct products. We deal with a special case of semidirect productwhen the twisting homomorphism acts diagonally on a direct product, as well asfor the case when the extending group is a direct product. We give applicationsof these results in the case of generalized dihedral groups and classicdihedral groups $D_{2n}$. For $D_{2n}$ we give a complete description ofsemidirect decompositions and values of minimal permutation degrees.

Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups