Example of non-Abelian group with 4, 5, or 6 elements of order 2

Question

Is there any example for non-Abelian group in which has more than $3$ elements of order $ 2$, but has less than 7 elements of order $2$?

Answer 1

The dihedral group of order $8$ - the symmetries of a square is one such.

It has the identity element and two elements of order $4$ (clockwise and counterclockwise quarter turns). The other five elements are four reflections about axes of symmetry and a half turn - all of order 2.

Answer 2

Consider $D_4$ Dihedral group, non-abelian, $5$ elements of order $2$.