Does a completely reducible module have to be isomorphic to a finite sum of irreducible submodules?

Question

I suppose this is a question about the definition of completely reducible. A case I'm interested in specifically is when we have a group ring $FG$ with $G$ a finite group and $F$ a field with $\text{char } F \nmid |G|$ so that Maschke's theorem applies to say that every $FG$-module is completely reducible. Is there additional structure here (say, with the Artin-Wedderburn theorem) that makes the question true, even if it's not true in general?