  The decomposition group of an irreducible plane curve $X\subset\mathbb P^2$
is the subgroup $\mathrm{Dec}(X)\subset\mathrm{Bir}(\mathbb P^2)$ of birational
maps which restrict to a birational map of $X$. We show that $\mathrm{Dec}(X)$
is generated by its elements of degree $\leq2$ when $X$ is either a conic or
rational cubic curve.
