4. (GBR 1) Let $P$ be a set of 7 different prime numbers and $C$ a set of 28 different composite numbers each of which is a product of two (not necessarily different) numbers from $P$. The set $C$ is divided into 7 disjoint four-element subsets such that each of the numbers in one set has a common prime divisor with at least two other numbers in that set. How many such partitions of $C$ are there?
4. Each of the subeets must be of the form $\left\{a^{2}, a b, a c, a d\right\}$ or $\left\{a^{2}, a b, a c, b c\right\}$. It is now easy to count up the partitions. The result is 26460 .