Invariant solutions for equations of axion electrodynamics

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.