  Suppose that $G$ is a groupoid with binary operation $\otimes$. The pair
$(G,\otimes)$ is said to be a gyrogroup if the operation $\otimes$ has a left
identity, each element $a \in G$ has a left inverse and the gyroassociative law
and the left loop property are satisfied in $G$. In this paper, a method for
constructing new gyrogroups from old ones is presented and the structure of
subgyrogroups of these gyrogroups are also given. As a consequence of this
work, five $2-$gyrogroups of order $2^n$, $n\geq 3$, are presented. Some open
questions are also proposed.
