Crypto Algorithm Question - Substitution cipher involutory keys

I'm trying to figure out a problem:

How many involutory keys are in the substitution cipher?

I understand what an involutory key is; it's when E(E(x)) = x. I did a similar problem with the shift cipher in which the result was k=0, 13 (for n = 26). Also, just playing around with the substitution cipher, I noticed that if the cipher text is equal to the plain text (basically, abcdefg...) or if the cipher text is equal to the reverse of the plain text (zyxwvut...), it achieves a E(E(x)) = x.

Any ideas? Maybe, I wasted time with the alphabet reversal and stuff, but feel free to point me in the right direction