  We generalise the construction of $Q$-family of quandles and $G$-family of
quandles which were introduced in the paper of A. Ishii, M. Iwakiri, Y. Jang,
K. Oshiro, and find connection with other constructions of quandles. We define
a composition of quandl's structures, which are defined on the same set and
find conditions under which this composition gives a quandle. Further we prove
that under this multiplication we get a group and show that this group is
abelian.
