I will present a classification result for subgroups of the outer automorphism group of a free product $G=G_1*...*G_k*F_n$, analogous to Ivanov's decomposition theorem for subgroups of the mapping class group of a closed hyperbolic surface of finite type. The main tool in the proof is a description of the Gromov boundary of the free factor graph of a free product, which is a hyperbolic graph on which this outer automorphism group acts. This is joint work with Vincent Guirardel.