已知集合 $A=\left\{n \left\lvert\, \frac{n}{3} \in \mathbf{Z}\right.\right\}, B=\left\{n \left\lvert\, \frac{n}{4} \in \mathbf{Z}\right.\right\}, C=\left\{n \left\lvert\, \frac{n}{6} \in \mathbf{Z}\right.\right\}$, 则
A. $A \cap B \varsubsetneqq C$
B. $B \cup C=A$
C. $C \varsubsetneqq A \cap B$
D. $B \cap C \varsubsetneqq A \cap B$