Let $X$ be a smooth connected projective curve defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G\;$be a finite group whose order is divisible by $p$. Suppose that $G$ has a normal $p$-Sylow subgroup. We give a necessary and sufficient condition for $G$ to be a quotient of the algebraic fundamental group $\pi_{1}(X)$ of $X$.