Constructing Lie group from Lie algebra

Question

I have a 3-dimensional real Lie algebra given by the relations: \begin{equation} [e_1,e_2] = e_2-2e_3\end{equation} \begin{equation} [e_1,e_3] = 2e_2+e_3\end{equation} \begin{equation} [e_2,e_3] = 0\end{equation} I need to describe some Lie group with such Lie algebra as a subgroup in $GL(3,\mathbb{R})$ In the first point of the task, it was necessary to find all the ideals and I did it, but I don't know how this can help in solving the second point.