The paper classifies primitive groups with dihedral point stabilizers and shows that for symmetric designs with dihedral or abelian local action, point and block stabilizers are conjugate in G, with G either imprimitive on points and blocks or a Frobenius group of odd order.
Wang, The primitive permutation groups with a dihedral subconstituent of order 2p, Acta Math
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Locally dihedral block designs and primitive groups with dihedral point stabilizers
The paper classifies primitive groups with dihedral point stabilizers and shows that for symmetric designs with dihedral or abelian local action, point and block stabilizers are conjugate in G, with G either imprimitive on points and blocks or a Frobenius group of odd order.