Denote by \(C(G)\) the conjugacy classes \([H]\) of subgroups \(H\) of \(G\), and define \([H_1] \leq [H_2]\) if and only if \(H_1 \leq H^g_2\) for some \(g\in G\). This preordering is an order relation for some \(G\) (but not all) and attention is restricted to this case (i.e., \(C(G)\) is a partially ordered set or poset). The notion of distributivity in posets is weakened to yield the definition of predistributive posets and the authors obtain an analogue of a result of Ore. Theorem A. For a finite group \(G\) the following are equivalent: (i) \(C(G)\) is predistributive, (ii) all Sylow subgroups of \(G\) are cyclic, (iii) \(C(G)\) is isomorphic to the lattice of all divisors of \(|G|\), and (iv) \(C(G)\) is a direct product of chains. Similar results are obtained in two other classes of groups for which \(C(G)\) is a poset.