  Using the three-dimensional subalgebras of the Lie algebra of Poincar\'e
group an extended class of exact solutions for the field equations of the axion
electrodynamics is obtained. These solutions include arbitrary parameters and
arbitrary functions as well. The most general solutions include six arbitrary
functions. Among them there are bound and square integrable solutions which
propagate faster than light. However, their energy velocities are smaller than
the velocity of light.
