"A relatively free lattice with $n$ generators has exactly $n$ maximal sublattices, each obtained by removing one of the generators (which are doubly irreducible). Thus there exist arbitrarily large finite lattices with only 3 maximal sublattices."
Can anyone give an example of this kind of lattice, or some pointer about what is a relatively free lattice and how to generate one?
The quote is from Maximal Sublattices and Frattini Sublattices of Bounded Lattices, see http://www.math.hawaii.edu/~ralph/Preprints/maxfinal.pdf