What was the relationship between the Heaven and Earth Society and the Red Flower Society in Jin Yong's novel?

The Heaven and Earth Society and the Red Flower Society were both characters in Jin Yong's novel, Book and Sword Gratitude and Revenge. The Heaven and Earth Society was a traditional martial arts sect that originated from the Ming Dynasty with the principle of "justice between heaven and earth" and "harmony between heaven and earth". Its members were mainly martial arts heroes and martial artists. The Red Flower Association was a Jianghu sect made up of female members. Its purpose was to "let a beautiful woman smile and settle grudges". Most of the members were beautiful women and women with strong martial arts. In the novel, there was a complicated relationship between the Heaven and Earth Society and the Red Flower Society. The Heaven and Earth Society and the Red Flower Society had conflicts with other sects in the pugilistic world, and they had worked together to deal with some enemies. In addition, there was a certain connection and cooperation between the Heaven and Earth Society and the Red Flower Society. For example, in some plots, they had planned some actions together.