I use to belong to a big group, we would get 200 plus people. I live in a city of 5 million people. Newcomers could easily get lost. After the meeting I was always busy with sponsees, or treasurer duties, or putting chairs away. I tried to talk to the newcomer as much as possible but it wasn't easy. HOWEVER I always went for coffee/dinner after the meeting (Fri. night meeting). Anyone was welcome to join me.
I would suggest that you start talking to people who are active in your group. The Treasurer, Secretary, Group Director/Master Chair etc. I bet they go for coffee after the meeting. The other thing you can is go to lots of meetings. You will meet many more people, and you are more likely to meet people who share your outside interests.
I rarely go to meetings anymore (still sober) but I have still have a host of friends from the fellowship. I met my best friend from AA.