  We consider a permanent magnetic dipole in an oscillating magnetic field.
This magnetic oscillator has two dynamical symmetries. With increasing the
amplitude $A$ of the magnetic field, dynamical behaviors associated with the
symmetries are investigated. For small $A$, there exist symmetric states with
respect to one of the two symmetries. However, such symmetric states lose their
symmetries via symmetry-breaking pitchfork bifurcations and then the
symmetry-broken states exhibit period-doubling transitions to chaos.
Consequently, small chaotic attractors with broken symmetries appear. However,
as $A$ is further increased they merge into a large symmetric chaotic attractor
via symmetry-restoring attractor-merging crisis.
