It is proved that for all positive integers with there is a positive integer such that every graph with edge density at least and at least vertices contains a -connected subgraph on at least vertices, or pairwise disjoint subgraphs with edge density at least . By a classical result of Mader [W. Mader, Existenz -fach zusammenhängender Teilgraphen in Graphen genügend großer Kantendichte, Abh. Math. Sem Univ. Hamburg, 37 (1972) 86–97] this implies that every graph with edge density at least and sufficiently many vertices contains a -connected subgraph with at least vertices, or pairwise disjoint -connected subgraphs. Another classical result of Mader [W. Mader, Homomorphiesätze für Graphen, Math. Ann. 178 (1968) 154–168] states that for every there is an such that every graph with edge density at least contains a minor isomorphic to . Recently, it was proved in [T. Böhme, K. Kawarabayashi, J. Maharry, B. Mohar, Linear connectivity forces dense minors, J. Combin. Theory Ser. B (submitted for publication)] that every -connected graph with sufficiently many vertices either has a topological minor isomorphic to , or it has a minor isomorphic to the disjoint union of copies of . Combining these results with the result of the present note shows that every graph with edge density at least and sufficiently many vertices has a topological minor isomorphic to , or a minor isomorphic to the disjoint union of copies of . This implies an affirmative answer to a question of Fon-der-Flaass.