Major Faction
The symbolic significance of the twin suns—as in the example here from Tatooine—is in the literal separation of loyalty and authority. In the symbol which represents the unaligned ‘faction’, it is the smaller whole which separates the larger whole; an individual forging their own straight path among the larger society.
Throne World: not applicable
While the Galactic Empire dominates the Core Worlds, and a variety of Underworld figures control much of the Outer Rim, throughout the entire galaxy still roam a great many individuals who do not hold loyalty to any faction whatsoever. These principled—or sometimes entirely unprincipled—individuals are known as Unaligned. In other words, they have no faction.
Unaligned entities may be unwilling to commit to a particular cause, or be disdainful of any other faction they might have cared to be associated with. In many cases, those who appear to be unaligned may in fact simply be hiding their true loyalty behind a veneer of neutrality, staving off threats or aggression from potential adversaries by appearing not to have any skin in a particular fight. Sometimes the unaligned are those who have become jaded by endless conflict, or have abandoned a faction they were previously associated with.