Determinability of a completely decomposable rank 3 group by its automorphism group

In the work of Vildanov, Gaidak, and Timoshenko, all completely decomposable groups of rank 2 were found that are defined by their automorphism group in the class of all completely decomposable groups. In this article, a similar problem is solved for groups of rank 3. It is shown that a completely decomposable group of rank 3 is determined by its automorphism group if and only if it is a direct sum of three almost divisible summands of rank 1, two of which are isomorphic to each other and embed into the third.