Quicksort has a complexity of Omega nlogn, Theta(nlogn) and bigO n^2.

An algorithm taking Theta(n log n) is far preferential since it takes at least n log n (Omega n log n) and no more than n log n (Big O n log n) but with quicksort this is not the case, is my definition of theta wrong? Should quick sort use little o n^2 to be more percise with its upper bound? Can theta be a one sided tight bound?