Thanks for any help or comments.

Suppose that $G$ is a finite group. A *Carter subgroup* of $G$ is a nilpotent
self-normalizing subgroup of $G$. Carter and Vdovin have shown that solvable
groups have Carter subgroups, and that in addition, in every group with
Carter subgroups, the Carter subgroups are conjugate -- see

Carter, R. W. (1961), *Nilpotent selfnormalizing subgroups of soluble
groups*, Mathematische Zeitschrift,
75 (2): 136–139.

Vdovin, E. P. (2006), *On the conjugacy problem for Carter subgroups.
(Russian.)*, Sibirsk.
Mat. Zh., 47 (4): 725–730. Translation in Siberian
Math. J. 47 (2006), no. 4, 597–600

Vdovin, E. P. (2007), *Carter subgroups in finite almost simple groups. (Russian.)*, Algebra i Logika, 46 (2): 157–216.

My question is about the structure of groups whose Carter subgroups are their Sylow $2$-subgroups? I mean, I am interested in any theorem which guides me towards some classification of this type of groups.