It's frustrating, to say the least. I don't know why it happens, but I've wondered myself if I've been invited to do things with groups just out of social etiquette.

There have been times when I have enough energy to play the part of someone I'm not in group situations. In those times, I'm talkative, funny, and I go out of my way to ask others about themselves. This is the fastest way to make people engage with you.

BUT. I don't have the energy for that usually. I don't like feeling fake like that. It's disheartening that my true self seems to be ignored in group settings. I've seen this happen with quite a few reserved people, so you definitely aren't alone in this feeling.