Just as the Justice League and Justice Society had satellite headquarters, albeit very briefly for the latter, the same could be said for their arch-enemies as well.
The Injustice Gang's inaugural appearance was prompted by the mysterious Libra recruiting six other supervillains to battle Earth-One's League and thereby acquire their powers for himself. The Injustice Society, or rather two members of its first incarnation... Brain Wave and Per Degaton... joined forces aboard the former's satellite headquaters. His goal? To acquire energies from Earth-Two exerted by young members of the Justice Society of America to gain a superhuman body for himself!
However the story of Libra parallels another tale from the Justice Society's old case files. Doctor Egri had harnessed cosmic radiation and focused it into six objects, which he arranged six criminals to steal and field test against the Justice Society. The gang leader, Rocky Castle, gained a magnetized ring like Green Lantern's; Specs had a black light to face Doctor Mid-Nite; Ox wore stick pin that allowed him to fly like Hawkman; Peewee wore gloves giving him superstrength like the Atom; Gun-Shy had a wristwatch that protects him much like Wonder Woman's bracelets; and Slowpoke donned a jacket giving him superspeed like the Flash. These crooks were eventually beaten by the Society and then trapped by Egri, who regained the devices to battle the combined team.
This may remind us of the Lawless League, created by that world's Johnny Thunder on an alternate timeline that spawned the Earth-Two world of Earth-A. His gang of crooks gained powers comparable to the Justice League and also, like the Rocky Castle Gang, battled the Justice Society. These included Monk Loomis, possessing a power ring like Green Lantern's; Bill Gore assuming the mantle of the Batman; Eddie Orson acquiring the powers of Martian Manhunter; Barney Judson now appearing as the Atom; Ripper Jones becoming a new Superman; Race Morrison gained superspeed like the Flash. The original members of Thunder's gang were the counterparts of Castle's gang, although their Lawless clones were the counterparts to the Bizarro Justice League.
But returning to Libra, this rogue manipulated matters through his six criminal cronies to siphon the superhuman energies from Superman, Batman (?), Flash, Green Lantern, Aquaman and Elongated Man... in much the same manner as the aforementioned Professor Egri. However, the result proved disastrous for each as their human bodies could not contain the combined six-fold energies, and they exploded/evaporated into nothingness!
And thus, a twice-told-tale intermingled in several stories but with the same conclusion!