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I've understood it the same way. We have fraternities and sororities. A gender-neutral term would be a social club.

However, I've just looked it up in Merriam Webster, and it looks like this term can include female members, too, even thought the word and the related adjective have strong masculine associations. Wikipedia basically says the same, "Although membership in fraternities was and mostly still is limited to men, ever since the development of orders of Catholic sisters and nuns in the Middle Ages and henceforth, this is not always the case. There are mixed male and female orders, as well as wholly female religious orders and societies, some of which are known as sororities in North America."