This is one of those oddball cases where DC actually thought about the continuity problems raised by a story idea, came up with a solution, and then promptly forgot about it, causing continuity problems for years to come.
Linda Lee runs into several super-powered youths like herself who clearly know her secret identity. It turns out that they are members of the Legion of Super Heroes, who had by this point made a pair of guest appearances in Superboy stories. Apparently realizing that there might be continuity issues, the Legion introduced in this story was purported to be a new Legion, comprised of the children of the original Legion. However, in all future stories Supergirl is a member of the same Legion that Superboy belongs to. The continuity problem comes in that if Superboy has met Kara, then he will not be surprised when she pops out of the rocket when he is a man. It was later explained that Saturn Girl leaves a post-hypnotic suggestion erasing his memory of Supergirl whenever he returns to the Smallville era.
The story borrows quite often from the original Legion story in Adventure #247, as I have discussed in the past. In an amusing twist, Red Kryptonite affects Supergirl by turning her into a woman; according to the Legion by-laws this makes her ineligible for Legion membership.