I understand how you feel - I have only ever had two or three close friends at a time, and I don;t find enjoyment in large groups of people together.
I do think you have to see this from a different perspective to help you deal with it.
The dynamics of inter-group relationships were all drawn and sorted before you arrived, so you really shouldn't fret about who includes whom or not when you are just a member of the group.
If you feel lost in a big group who know each other, why not develop a closer relationship with one or two of them - this should happen naturally, no point trying to force it.
Then you can see your closer friends individually, or perhaps a couple at a time, and do something you like to do, and then you'll find the bigger gatherings less stressful.
As the 'new kid on the block' it's very easy to feel left out and uncomfortable but you will settle down and relationships will ebb and flow with you, and around you.
If you don't take responsibility for everyone feeling OK, then you won't worry if things seem not to work. It is very easy to take on this burden if you are a sensitive caring soul, but the clue is there - you take it on yourself.
So drop it!
You'll feel a lot more relaxed, and the pressure you feel will start to vanish.