Finite permutation groups with a regular dihedral subgroup, and edge-transitive dihedrants

We study finite permutation groups that contain a regular dihedral subgroup, called d-groups. In particular, a classification is given of bi-quasiprimitive d-groups. It is then applied to classify edge-transitive dihedrants of order 2pm and valency coprime to p, where p is an odd prime and m is a positive integer.