On exact products of two dihedral groups

An exact product of two finite groups $H$ and $K$ is a finite group $X$ which contains $H$ and $K$ as subgroups, satisfying $X=HK$ and $H\cap K=\{1_X\}$. In this paper, we provide a classification of the exact products of two dihedral groups of orders $2m$ and $2n$ for all odd numbers $m,n\ge 3$.