The group 2H_2 has four distinct (oriented) reflections x -> x' = rxr, rr=1.
Each reflection is characterized by the unit direction vector r of the line of reflection.
These reflections are oriented, because each line of reflection has two possible opposite directions,
characterized by the sign of the unit direction vector r.
r = a
r = -a
r = b
r = -b
Each reflection can be visualized by dragging the red vector perpendicular to the line of reflection to a particular value of r. It is easily verified that any other choice of r, not in the above list, will not produce a reflection symmetry of the symmetric bar. The combination of two such reflections at r and r' will yield an (oriented) rotation y->R~yR=(r'r)y(rr') from the dicyclic group 2C_2.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).