It is known that if the group \(G\) is the product of finitely many pairwise permutable cyclic subgroups, then \(G\) is supersoluble [see H. Heineken and J. C. Lennox, Arch. Math. 41, 498-501 (1983; Zbl 0509.20017)]. Moreover, M. J. Tomkinson [ibid. 47, 107-112 (1986; Zbl 0596.20026)] proved that, if the factors are Chernikov and locally cyclic, then \(G\) is hypercyclic. In this paper the author proves that if the group \(G\) is the product of finitely many pairwise permutable subgroups which are minimax and locally cyclic, then \(G\) has a finite normal series with locally cyclic factors. Moreover, if the factors are not torsion-free non-cyclic groups, then \(G\) is hypercyclic.