From the Iconoclasts to Spacer's Choice there's a number of different The Outer Worlds factions that you can interact with and influence during your journey. You'll stumble upon a plethora of interesting characters with a variety of motives and stories in The Outer Worlds, and it's down to you to increase or decrease your reputation with them based on your actions. If only for the reduced vendor prices you'll get when they like you. Here are all of The Outer Worlds factions and where you can find them.
Don't worry about spoilers here either, as I'll keep everything completely spoiler-free!
"It's not the best choice, it's Spacer's Choice!". Spend too long in Edgewater or Groundbreaker and the Spacer's Choice jingle will be drilled into your memory like lyrical tinnitus. Spacer's Choice is the popular budget brand producing masses of saltuna in Edgewater, which is where you'll find this faction and most accompanying quests.
The Deserters are a group of people who became disillusioned with the management of Edgewater town, so fled to start their own community in the nearby Botanical Lab. You'll meet these folk early on in the game, when you speak with their leader, Adelaide.
As you'd expect, the Groundbreaker faction can be found on board the Groundbreaker ship. Junlei Tennyson leads this group of space-residing crew, and they're the only township operating outside of the control of the Board. There's plenty to find and discover aboard Groundbreaker, despite it being a ship and not a full planet.
SubLight Salvage & Shipping
SubLight Salvage & Shipping can be found all over the Halcyon system, but their base of operations is on Groundbreaker. They're essentially a facade of a company that uses their guise of waste disposal and transportation to operate illegally in more questionable areas, but despite this, you're going to want to get on their good side.
The Halcyon Holdings Board of Directors (or just The Board for short) are the ones who rule over the Halcyon system, maintaining the peace where they can. They're comprised of CEOs from each of Halcyon's founding companies with Chairman Rockwell leading them, and you'll be dealing with The Board plenty throughout the entire game.
When you head to Roseway on Terra-2, you'll find the Auntie Cleo family. Ditched and forgotten by The Board, Auntie Cleo focuses on "scientific research and advancement" with things like their "Auntie-Biotics" line of medicinal solutions and Tripicale foodstuffs.
Monarch Stellar Industries
Head on over to Monarch to find Monarch Stellar Industries, a company that was once Board-owned but has since split to be privately owned. Sanjar Nandi is the leader and you'll find these folk mainly around Stellar Bay, the first town you'll visit on the planet.
Much like the Deserters on Terra-2, the Iconoclasts are a community that split from Monarch Stellar Industries and made their home in Amber Heights. Led by both Graham and Zora, the pair often bicker but share the same goal of "tearing down the corporate establishment that they believe has brought the colony to the brink of death."
C&P Boarst Factory
The C&P Boarst Factory is responsible for the processing of Cystypigs, which are a curious delicacy in the Halcyon system. You'll find the facility on Monarch and you'll venture in there as part of the Slaughterhouse Clive quest, during which you can influence your reputation with them. Will you err on the side of caution with the Boarst King?