I just walk up to the edge of the group and listen. Usually the group will shift a little to make room. If not, I just hang out there. If they have a problem with me joining them they can tell me. It is very impolite to have private conversations in public, especially at a social event where mingling is normal behavior.
Often it seems my comments are ignored. Once, hours later, I awkwardly asked someone (who knew I was autistic) if they heard what I said. They said yes, and told me it is normal that sometimes responses are not given and that I should not repeat myself.
To leave the group, I make an excuse like going to get a drink, or mingling with others. If I don't want to interrupt, I just walk away and let them wonder. If they ask, I use the excuses listed above.
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When I lose an obsession, I feel lost until I find another.
Aspie score: 155 of 200
NT score: 49 of 200