Flying

From Hpwiki

Flying is one of the magical courses taught at Hogwarts, but only in the first year. The wizards and witches do not really fly, they ride Broomsticks, and these Broomsticks do the flying. In other words, don't fall off.

Naturally, Flying and Quidditch are always closely related. So it's obvious that Madam Hooch, the Flying teacher at Hogwarts, is also responsible for Quidditch organization.