  This paper considers how many conjugacy classes of reflections a map can
have, under various transitivity conditions. It is shown that for vertex- and
for face-transitive maps there is no restriction on their number or size,
whereas edge-transitive maps can have at most four classes of reflections.
Examples are constructed, using topology, covering spaces and group theory, to
show that various distributions of reflections can be achieved. Connections
with real forms of algebraic curves are also discussed.
