  In 1869, Jordan proved that the set $\mathcal{T}$ of all finite group that
can be represented as the automorphism group of a tree is containing the
trivial group and it is closed under taken direct product of groups of lower
order in $\mathcal{T}$ and wreath product of a member in $\mathcal{T}$ and the
symmetric group on $n$ symbols. The aim of this paper is to continue this work
and another works by Klav$\acute{\rm i}$k and Zeman in 2017 to present a class
$\mathcal{S}$ of finite groups for which the automorphism group of each
bicyclic graph is a member of $\mathcal{S}$ and this class is minimal with this
property.
