You can draw a line through either the vertical or the horizontal set of arrow points, and the figure can be reflected about that line with no change. Those are lines of symmetry.
You can draw diagonal lines through either the north-east/south-west set of internal corners or the north-west/south-east set of internal corners, and the figure can be reflected about that line with no change. Those, too, are lines of symmetry.
You can rotate the figure 90°, 180°, or 270° (or 360°) in either direction about its center. Those are 4 orders of rotational symmetry.
The figure has 4 lines of mirror symmetry and order 4 rotational symmetry.