A quandle is a self-distributive algebraic structure that appears in quasigroup and knot theories.For each abelian group A and c ∈ A, we define a quandle G( A, c) on ‫ޚ‬ 3 × A. These quandles are generalizations of a class of nonmedial Latin quandles defined by V. M. Galkin, so we call them Galkin quandles.Each G( A, c) is connected but not Latin unless A has odd order.G( A, c) is nonmedial unless 3 A = 0. We classify their isomorphism classes in terms of pointed abelian groups and study their various properties.A family of symmetric connected quandles is constructed from Galkin quandles, and some aspects of knot colorings by Galkin quandles are also discussed.