As there have always been since the rise of Human Culture, there are elements in a society that go, radically, against the status-quo - Often dubbed as Terrorists due to their usage of fear and terror to bring about their goals, these people are just as common in the 26th Century. Some of these groups have taken up activities in the Nyx System, where you are located for your work aboard whichever vessel or Outpost.
Not only are there terrorist organizations though. Crime Syndicates, Illegal Corporations, and many other illicit groups take part in these acts of terror so as to get people, specifically you, to do what they want.
Currently in the Nyx System, there are most likely around 300 different subversive groups that are taking action against the powers that be. Of those 300 or so, 6 of them are quite powerful and often take part in bombings, public executions, assassinations, and other forms of violent activities. Those groups are as follows:
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[Fury of Mankind](http://baystation12.net/lore/Subversive Elements/FOM): A Human Supremacist group based originally out of Mars, the group has in recent years taken an interest in Nyx due to the high population of Aliens working and living there. Many lynchings have occurrred on the various colonies and stations against Unathi, Skrell, Resomii, and Tajara in the name of Humanity.
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The Luddites: Based entirely out of Nyx, the Luddites take their name from an Industrial Era group of rebels and anarchists who were against the continual rise in technology. In recent years due to the rise of IPCs and other technology (such as Phoron-based tech, and Supermatter Engines), they have taken up terrorism in the system so as to remove the prescence of Technology in Society.
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Orlowskaja Gruppa: The Orlowskaja Gruppa is an old-world organisation, part of the human underworld. They are of Eastern-European origin. "Russian Mafia" as they were called in the past. They are mainly located on Earth and Mars. Though they have spread over most Sol Planets. They're led by a cruel man, named "Stepan Orlow" or "Brother Stepan" for those who know him. He's known to loose his temper real quick... and when he does, bad things follow. They've recently taken up activity in Nyx due to the rise in the Drug Trade there and nearly empty market that they can monopolize.
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Cyber Jacks: Cyber Jacks are an aug-legging group, mostly operating out of Sol. They like to steal people off of the streets and explain in good detail why they should let them take their cybernetics, usually with the help of a surgical saw. They are, surprisingly, rather good at what they do, able to get it all removed clinically, and then they throw their prey back out onto the street if they aren't too dead. It is currently unknown as to whether they operate in Nyx, but there have been many Cybernetic thefts throughout the system.