when my ds1 was 6 he used to do karate, football, trampolining, beavers after school and swimming and horse riding at the weekend. this was all his choice, generally he had a friend who went to one and he wanted to go with him/her. and karate was three time a week with his dad. so he was very busy, too busy i would def say, but if i ever suggested not going to one of the clubs he would get really upset and so i would always let him go, but in the last year (hes now 8yo) he has given up all of his activities.
i find this very sad as i kow he needed to cut down, both interms of his time and the finacial and time cost that was involved, i think approx three activities a week are enough for most children of that age and i probably wouldn't include the lunch time activity as these are in school time and most of her friends probably go to them too.
i would say that if she was happy then let her continue as long as you have the time and money for her to do these activities, just don't be surprised if as she gets older she may want to quit one, some or all of them. apparently its a phase that a lot of older kids go through.