I'm reading the first chapter of Serre's Galois Cohomology.
On p. 58, He gives two examples of projective profinite groups:
(a) the profinite completion of free (discrete) groups; (b) the cartesian product over all prime numbers of free pro-p groups.
Looking for other examples I understood solvable projective profinite groups.
Mimicking the construction of projective covers for modules, I found the concept of the projective cover of a profinite group.
Now I'm stuck!
Any suggestions of more examples of projective profinite groups?
EDIT: Actually I'd like to see f.g. profinite groups. So, in other words, I want to know the f.g. closed subgroups of free profinite groups.