In this work the authors develop a decomposition theory for subgroups of $mathsf{Out}(F_n)$ which generalizes the decomposition theory for individual elements of $mathsf{Out}(F_n)$ found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.

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