P-constrained not implies Glauberman type for p

This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., p-constrained group) need not satisfy the second group property (i.e., group of Glauberman type for a prime)
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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