I've never, ever felt like a core part of any group outside my family. The closest I've ever been is the dojo, and it's taken years to get that far. Even if I'm the one who brought a group together, I feel like I'm on the edge of it, and there have even been occasions where I've ended up being dropped from groups like that. Extravert or not, I don't gel perfectly with a group. I bend some, but there is a core Ironphoenix-ness which doesn't bend to suit the crowd.
Some groups learn to accept me as I am more than others, and those are the ones I stay with for any length of time. Some groups mutate enough that I can effectively move from group to group just by letting others come and go. But I just about always feel a gap. I sometimes feel that I'm my own in-group, of one. I'm fortunate in having the self-confidence to be able to see it that way (most of the time) rather than descending into feeling that I'm my own out-group, of one: that way lies paranoia.
God, family, close friends, and aikido are my only real ways out of that. My social time does fulfill a need, and it is the real me that participates in that, but there are sides of me that don't usually come out then, and that sometimes jump out at me as I close the door behind the last guest or wave goodbye and saunter off. That's when those closer connections matter, and I think that everybody experiences those moments when it feels like none of those usual connections are available.
The only one of the four I mentioned that is always there if I think to seek it, and if I open myself enough to accept it, is connection with God. Not everyone has this experience, and I'm not going to try to guess whether it's God's will or our choices which make it so, but for me, that's the real last line of defense.
I'm not sure whether I ended up accomplishing what I originally set out to do, but, as a famous outsider said, "quod scripsi scripsi."*
*: "What I have written, I have written."