So if there were a group of people in the states that had "special powers" that made them a potential threat, who would investigate them? FBI? CIA? Homeland Security? By potential threat I mean control over some politicians, maybe the head of some mafia type activities, or maybe they're just a harmless secret community that happens to be larger than one would think. I hope this is making some sense, I've had zero coffee this morning so if you need further clarification let me know.
Google the 3 agencies to identify their missions. My guess is that Homeland Security & FBI would both be involved to investigate and battle against the threat, but then CIA would come into the picture to investigate any outside (of the U.S.) involvement.
You could even have the government set up an alternative agency to deal specifically with the "threat", and have it made up of members from the three other, real-world, agencies.
Basic break down is as follows: FBI - Deals with crimes that cross state borders. Otherwise, those crimes are deligated to local authorities, but when a crime crosses state lines, it falls under FBI jurisdiction, so as to streamline both local agencies. Control over politicians and Mafia connections CIA - Deals with foerign affairs. America's "spy" agency and would probably deal with a foerign national with powers comitting a crime against the United States. If it's a US citizen on US soil, then it doesn't concern the CIA. NSA - Threw them in because their misuse in fiction peeves me. NSA is the "eyes and ears" of the intelligence community. Their (official, because they are Uber secretiv) job is to listen to foriegn chatter and figure out what they are saying. Most of their uses in fiction, especially United States produced, have them as a spy agency akin to the CIA or the "real" power in the United States. Both are not true and the actual job is not as glamorous. FEMA - Another Throw in, these guys are currently one of the most well known branches of Homeland Security, and are in charge of disaster relief. If one of you super-powered bad guys really went ballistic, they would be the people who helped with the clean up. Department of Homeland Security - Along with FEMA, they include the departments Citizenship and Imigration, Customs and Borders, Imigration and Customs enforcement, Trasnportation Security Administration (TSA), The Coast Guard (during times of war, or Presidential disgression, this department falls under the Department of the Navy), and the Secret Service (in addition to protecting dignitaries, they also handle counterfitting of currency, which was their original stated purpose). They may likely have a department of superhuman affairs in your story, but so far, they seem more concerned with movement of people and goods internally and externally.
It would almost certainly be the FBI. But also remember there are several very covert Special Operation Forces in the United States Military (Delta, SEAL Group 6, etc) that have very vague roles. If something of that magnitude happened, I wouldn't be too terribly surprised if Delta's/Group 6's expertise was called in to handle whatever needed to be done. But if you want a specific agency, probably the FBI.
Probbably the CIA. FBI seem to handle gangs and smaller number crimes like serial killers. Homeland Security might, but I'd say that the CIA would handle the bigger targets. Just my thought though.
It would depend on how the threat is posed by this Group and how well they are known. For example, if they just sat around and didn't do anything, not posing any threat, no one would investigate them. Also depending on the level of the threat as has been mentioned it may be interesting to introduce a new organization composed of the 3 major organizations to combat/investigate/deal with the Group; however this may seem too "superhero"-esque. Depends on what you want from your story, I suppose.
The dangerous group is Congress! Vote NO on incumbent. It's the only way to control them. As far as investigating them, I'm afraid there's no hope...LOL
alphabetacracy soup It depends on how pervasive the influence of this group was perceived to be. Remember that Al Capone was eventually jailed for tax evasion, investigated by the US Treasury Department, not the FBI. There are also quasi federal enforcement bodies such at the ATF , who seem to have their dirty fingers in almost every pie these days, regardless of their charter. If this groups 'special powers' were granted through public office or their actions involved violation of the 'interstate commerce act' they would initially fall under the auspices of the FBI. If they had foreign associations, funding, members or assets they would be scrutinized by the CIA but domestic investigation and prosecution would be left to the FBI. -- If your group is really powerful, backed by a foreign government or it was believed that federal officials had been compromised there would be congressional or senate hearings and a special committee, or subcommittee formed to probe the problem in secret. This committee would make use of combined resources gathered by the domestic intelligence and enforcement alphabetacracy (CIA NSA FBI DHS ATF IRS, did i leave one out?) and name themselves something uniquely amero-bureaucratic like "The Congressional Special Committee on <your groups> affairs." Take a look at the era of McCarthyism (red-scare). It might help to establish a model for what might happen if the threat perceived was sufficient to threaten the 'roots of democracy'.
Ok I haven't decided what exactly the scenario is but I'm thinking along the lines of this: An overeager agent of (some government agency) accidentally stumbles onto an underground group of people with special "capabilities". As he digs deeper he finds out that one of these guys has some questionable connections to some important/powerful people and might have leverage over them. Basically, this has to potential to turn into a sort of witch hunt. So who would do the hunting? I don't even know how to find out. I'm wondering if I should just pick one and call it good. lol