I can tell you, without looking, that there are five natural types of changelings and five political groups they can sign on too... without ever glancing at the book...
And you'd be... wrong, as it happens. That "five by five" pattern only holds true for the Big Three:
Vampire,
Werewolf, and
Mage.
Changeling includes six Seemings and four Courts (in its core book, anyway, since the later supplements then went on to introduce at least eight additional Courts from around the globe). Furthermore, each Seeming (a kind of an extremely broad fairytale archetype) is divided into a number of optional subtypes called "Kiths", so that for instance a Beast might also be a "Hunterheart" or a "Skitterskulk", and a Darkling a "Gravewight" or a "Mirrorskin." It could be worth noting, too, that the Courts aren't necessarily so much political entities as protective pacts with various aspects of the natural world such as seasons or directions, although the members of each tend to have in common a specific basic attitude when it comes to dealing with the threat of Faerie. The Autumn Court studies fae creatures and magics in order to defeat the enemy with its own weapons, for example, while the Spring Court seeks to enjoy the fullest possible life here and now.
You're forgetting the so-called social "z-axis" of the splats, by the way: Bloodlines for vampires, Legacies for mages, and so on. For changelings, that's Entitlements, noble orders with their own requirements and privileges. The core book features nine of them, from the Bishopric of Blackbirds (counsellors who safeguard the sanity of other changelings) to the Tolltaker Knighthood (glorified bounty hunters for any supposedly good cause).
But it's actually possible to put together a Lost PC who doesn't belong to any of those groups, though. Joining Courts or Entitlements is completely voluntary, and there's a two-dot "No Seeming" Merit which does exactly what it says on the label.