The group 2H_4 has eight 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, aba ... blue
r= -a, -aba ... light blue
r= b, bab ... green
r= -b, -bab ... orange.
Each reflection can be visualized by dragging the red unit direction vector of the line of reflection to a particular value of r. It is easily verified that other choices of r, not in the above list, will not produce a reflection symmetry of the square. 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_4.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).