A JW woman can have no position of authority in the congregation. For that matter, if a 12-year-old JW boy is baptized and he is the only male in a group of older women, HE is the one who will offer prayer, and, if they are going out in field service, HE is the one who will make the decisions.
If a JW woman is highly trained in a certain field, and is working with an inexperienced JW male in her field of expertise (as in, perhaps, some sort of building project) SHE will have to acquiesce to the inexperienced male, even though SHE is the one who should, logically, be leading the group.
The first "step up" for a JW male is to be assigned to handle microphones or do some other minimal "privilege" in the congregation. After that, he can be appointed as a Ministerial Servant, and then, possibly an Elder. Within the body of Elders, there are various positions, with Presiding Overseer being the top position at the congregation level.
There are many other titles within the JW hierarchy...all of which are reserved for men.