  An old problem raised independently by Jacobson and Sch\"onheim asks to
determine the maximum $s$ for which every graph with $m$ edges contains a pair
of edge-disjoint isomorphic subgraphs with $s$ edges. In this paper we
determine this maximum up to a constant factor. We show that every $m$-edge
graph contains a pair of edge-disjoint isomorphic subgraphs with at least $c
(m\log m)^{2/3}$ edges for some absolute constant $c$, and find graphs where
this estimate is off only by a multiplicative constant. Our results improve
bounds of Erd\H{o}s, Pach, and Pyber from 1987.
