  We classify maximal totally geodesic submanifolds in exceptional symmetric
spaces up to isometry. Moreover, we introduce an invariant for certain totally
geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin
index. We prove a result analogous to the index conjecture: for every
irreducible symmetric space of non-compact type, there exists a totally
geodesic submanifold which is of minimal codimension and whose non-flat
irreducible factors have Dynkin index equal to one.
