$S=\{1,2,3..............12\}$ $A,B,C $ are disjoint equivalent subsets of $S$ so that $A\cup B\cup C=S$. How many such sets $A,B,C$ can be formed?

Question

$\begin{array}{1 1} (A) ^{12}C_4\times^8C_4\times^4C_4 \\ (B) ^{12}C_4\times^{12}C_4\times^{12}C_4 \\ (C) ^{12}P_4\times^8P_4\times^4P_4 \\ (D) 64 \end{array} $