Just overheard a couple of first-years arguing by the dorms about whether the Nightingale Duelist Society or the House of Obsidian has more clout this semester. That’s Gehenna in a nutshell; the rivalries aren't just clubs, they're entire micro-societies. The big one is obviously the Meritocrat faction versus the Old Blood legacies. The Meritocrats think magic and status should be earned through the brutal monthly gauntlet trials, while the Old Bloods, whose families basically endowed half the towers, think tradition and lineage are what keep the academy's wards intact.
Then there's the library cold war between the Archivists and the Practical Casters. The Archivists guard the restricted stacks like dragons, convinced every unverified spell is a catastrophe waiting to happen. The Practicals, mostly from the alchemy and battle-mage tracks, keep 'losing' permits and 'borrowing' grimoires for field experiments. You can always spot a Practical after a major raid—they have that singed-hair, slightly guilty look.
Smaller spats define daily life, too. The east-wing potioneers feud with the west-wing herbalists over who 'owns' the spectral moss in the courtyard grotto. It's petty, but it means the best restorative teas come from a clandestine midnight harvest trade. The rivalries shape everything, from who you sit with in the Refectory of Echoes to which secret passageways you're allowed to use. Honestly, without them, the place would just be a very pretty, very haunted castle.