There was a question on here today with some similarities to this. People are all different. Some are introverts who had rather spend a good deal of time alone than in groups or with friends. I was a lot like this as a child. I DID enjoy playing with other kids and I had friends from school, but more than anything I enjoyed playing by myself and reading for hours on end -by myself! I still do! As I got older and "blossomed" into a young woman during my teenage years, I did start enjoying going out more and dating and going to parties, etc. In fact, most anyone you asked who has known me for the past 25 years would NEVER say I was introverted! But a big part of me still is -I long for alone time. It's the thing I miss most from my pre-children days. And I don't mean a few hours -I mean days! It's just my personality. I have lots of friends and a really well-rounded life, but I was like your daughter. Don't push her too hard. Try to be more accepting of her personality. Be proud of the fact that she has a great imagination and can entertain herself. SO many kids are lacking that these days. I've ALWAYS hated "group activities" at school, and despise the push in all education to make everyone constantly work in groups. The excuse is that that's the way it is in the work world, and I don't find that to be true. You may be part of a "team" in many jobs, but you are usually doing your job on your own as part of a larger team. Let her know there are some activities and things in school she has to cooperate with, but also remind the teacher that not every child learns the same way -and that's why they're supposed to break up the day into different learning segments. You can start trying to find sports she enjoys and get her involved in something like that to help her with group work. I played a lot of sports -although the ones that were individual pursuits always suited me best.
Ask her if she would like to be in Girl Scouts or some type of class or social group where she might make some friends. She will eventually, but it is harder for introverted people. Just try to gently guide her instead of feeling like something is wrong with her. She WILL pick up on that!