Select elements from a list based on alphabetical order criteria

I have this code to generate the anagrams for a 6 letters word:

letters = {"P", "E", "R", "I", "T", "O"};perms = Permutations[letters, {6}];list = StringJoin /@ perms;

Which gives me 720 possible combinations as expected. I'd like to select among those only the ones for which the vowels (i.e.: E, I and O) occur in alphabetical order. For instance:

"PERITO", "PERIOT" and "PERTIO" would be valid cases but "PERTOI", "PEROIT" and "PEROTI" would not. How can that be done?