In this talk, we study almost normal subgroups from a geometric point of view. When a group G is equipped with a proper left invariant length, we characterize the subgroups H whose coset space G/H, with the induced metric, is a locally finite space coarsely embeddable into a Hilbert space. We will give examples that i find interesting : these are S-arithmetic groups with quite exotic properties. If time allows, we will present the main application : if H and G/H admit a coarse embeding into a Hilbert space, then G satisfies the Novikov conjecture.