The term " _family_ " is used for sets of sets. This usage is most common when all the elements of the sets in the family are of the same kind (So in your examples $D = \\{A,C\\} = \\{\\{1,2,3\\},\\{3,5,6\\}\\}$ is a more typical example than say $\\{A,B\\} = \\{\\{1,2,3\\},\\{\mathrm{blue},\mathrm{white},\mathrm{red}\\}\\}$). Wikipedia:
> In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.