I'm hoping someone else can help you with this. I've experienced it myself and with my dc's, but I don't have good advice, I think. We have waffled, ineffectually, between two approaches. One is to try to get dc to connect with others on their level. The conversation goes like this (dc at age 9 but basically it was the same conversation all the way through):

DC: But I can't talk to people at school. They aren't interested in anything interesting. No one else is [reading OLIVER TWIST or SOCIOLOGY FOR DUMMIES or wondering about bird evolution].

ME: Can't you talk to them about what they are interested in?

DC: But I don't care about [baseball, pop music, etc.]

ME: Sometimes we just have to get along. Sometimes we just make conversation.

DC: But it makes me tired. And they won't be my real friends if I'm just pretending.

ME: [silence]

The other approach is just to realize that life can be kind of lonely in this sense and just deal with it. That's kind of a big thought, though, for a kid. We have found a few camps and programs with great kids that dc can connect with at a high level through shared interests. But, as you say, that's not the same as having school-day connections.