# Order of product of subgroups

**Algebra**Level pending

Let \(G\) be a group and let \(H\) and \(K\) be two subgroups of \(G\).

If both \(H\) and \(K\) have \(12\) elements, which of the following numbers cannot be the the number of elements in the set \(HK\) ?

**Notation:**

- \(HK = \{hk\mid h\in H~\textrm{and}~k\in K\}\)