  A quandle is an algebraic structure whose axioms correspond to the
Reidemeister moves of knot theory. S. Kamada introduced the notion of a quandle
with a good involution, which is later called a symmetric quandle. We are
interested in the algebraic structure of symmetric quandles. Given a group $G$,
an element $z$ and a certain subgroup $H$, one can obtain the quandle. D. Joyce
showed that every quandle is isomorphic to the disjoint union of such quandles.
In this paper, given a group $G$, elements $z,r$ in $G$ and a certain subgroup
$H$, we construct a symmetric quandle. Futhermore, we show that every symmetric
quandle is isomorphic to the disjoint union of such quandles.
