1.6.92 Fields, Groups, Rings

condition: The Abelian group \( A \) contains as a subgroup \( \mathbb{Z} / 2 p \mathbb{Z}, \quad \) and the factor group on it is isomorphic to \( \mathbb{Z} / 2 q \mathbb{Z} \), and the numbers \( p, q \) are simple. What can the group \(A\) be isomorphic to? Consider all remaining cases.