Nontrivial semidirect product of cyclic Lie ring of order four and cyclic Lie ring of order two

Definition
The dihedral Lie ring of order eight is defined as the dihedral Lie ring with eight elements, i.e., the semidirect product of a cyclic Lie ring with four elements and a two-element subring whose non-identity element acts on the cyclic part via the multiplication by two map. In other words, it is given by the presentation:

$$\langle a,x \mid 4a = 2x = 0, [x,a] = 2a \rangle$$