This T'Pol photo contains
boater, leghorn, panama, panama hat, sailor, skimmer, straw hat, fedora, felt hat, homburg, stetson, and trilby.
There might also be
porkpie, porkpie hat, pith hat, pith helmet, sun helmet, topee, topi, dress hat, high hat, opera hat, silk hat, stovepipe, top hat, topper, and beaver.