I have a 1776-1976 half dollar, there is no "S" or any other letter on the front. There is a marking at the base of the neck, just above the "w" in we. On the back there are 3 letters "SGH". Is this of any significance?

SGH is simply the sculptors initials. Seth G. Huntington sculpted the Independence Hall on the reverse of the coin.
-M.