  In this article on the basis of a new definition of spacetime symmetry, which
is in accordance with the symmetry of the curvature invariants, we investigate
exact vacuum solutions of Einstein field equations corresponding to both static
and stationary plane symmetric spacetimes using the concepts of the
(1+3)-decomposition or threading formalism. Demanding the presence of a plane
symmetric gravitomagnetic field we find a family of two parameter (m and l)
solutions, every member of which being the plane symmetric analogue of NUT
space.
