  We study in a semiclassical regime a two-dimensional magnetic periodic
Schr\"odinger operator. We first review some results for the square (Harper),
triangular and hexagonal (case of the graphene) lattices. Then we study the
case considered by Hou when the periodicity is given by a kagome lattice. We
reduce the problem to the study of discrete and pseudodifferential operators
and obtain pictures similar to Hofstadter's butterfly. We prove the existence
of flat bands, which do not occur in the three previous cases.
