Generalized dihedral groups are strongly ambivalent

Statement

Let $H$ be an abelian group and $G$ be the Generalized dihedral group (?) corresponding to $H$. Then, $G$ is a Strongly ambivalent group (?): every element of $G$ is a Strongly real element (?). In other words, every element is either the identity element, or an involution, or the product of two involutions.

Related facts

• Classification of rational generalized dihedral groups
• Generalized dihedral groups are ambivalent
• Symmetric groups are strongly ambivalent
• Symmetric groups are rational