It is well known that a lattice is distributive iff it excludes as a sublattice $N_5$ (the pentagon) and $M_3$ (three unordered elements with a top and bottom). Further, a lattice that only excludes $N_5$ is modular, and consequently a lattice excluding $N_5$ but including $M_3$ is modular but not distributive.
What, if anything, is known about the class of lattices that excludes $M_3$? Does it relate to classes of structures of any particular interest? (Note this is not the same as asking about "nonmodular varieties", since those are varieties which include $N_5$).