P-constrained not implies Glauberman type for p

Statement
There can exist a prime number $$p$$ and a finite group $$G$$ such that $$G$$ is $$p$$-constrained but is not a group of Glauberman type for $$p$$.

In fact, we can find such a finite group $$G$$ for every prime $$p$$.

Related facts

 * p-solvable not implies Glauberman type for p
 * p-stable not implies Glauberman type for p
 * strongly p-solvable implies Glauberman type for p