Subgroups of profinite surface groups

We study the subgroup structure of the 'etale fundamental group $\mathrm{\Pi }$ of a projective curve over an algebraically closed field of characteristic 0. We obtain an analog of the diamond theorem for $\mathrm{\Pi }$. As a consequence we show that most normal subgroups of infinite index are semi-free. In particular every proper open subgroup of a normal subgroup of infinite index is semi-free.