There is something about the American Spirit, perhaps a curdling in the Melting Pot, Americans terrorizing other Americans is a recurring theme in our history.
Ku Klux Klan
At its apex in the 1920's, the Klan had four to five millions of members. Founded after the Civil War by former Confederate soldiers to resist post-war Reconstruction it quickly resorted to terrorist acts aimed at suppressing the freed slaves. Northern whites who organized schools for the freedmen, blacks who tried to start businesses, vote, or bear arms were targeted for intimidation or murder. People would be roused from their sleep at gunpoint by hooded raiders. The lucky ones would be threatened; the unlucky ones would be lynched or burned alive. One of the first anti-terrorism laws passed by Congress was the Klan Act of 1871.
The Klan faded in the 19th Century only to be reborn anew in 1915, in part due to the film Birth of a Nation. The new Klan expanded its hate list to include Jews, Catholics, unions, and Hispanics in western states like California, as well as black Americans. It grew to immense strength. In many areas of the country you could not get elected without ties to the Klan. Lynching and burning again became their terror weapons of choice. There has never been a larger, more successful, or more deadly terrorist organization operating within the United States.
Other sources: the mid-west's Black Legion, the African American Registry article, ADL.
Not a group but a tactic, lynching has been the preferred tactic in America for spreading terror in a population. Killing someone by hanging - men and women have both been lynched - was more than just murder. Often the victim would be tortured or burned while still alive. The bodies would be left hanging for days and even weeks while they rotted and were eaten by animals. The point was to terrorize.
The Klan in the south used lynching to punish blacks who tried to register to vote and as an object lesson to any who might consider voting in the future. As can be seen in this picture, lynching black Americans in southern states was a family recreation. Native Americans were frequent victims. In California lynching Hispanic Americans was so common Spanish slang in the state called American democracy "linchocracia."
There is still a lingering affection in some circles for lynching. In 2005, the Senate voted on a symbolic resolution condemning more than a century of the lynching of black Americans. Ten Senators, all Republicans, voted against the resolution.
Other sources: the American Institution of Lynching, Bob Geiger on the relationship between historical lynchings and modern Redstaters (scroll down to 6-16-2005).
Puerto Rican Nationalists
Pop quiz: What is the only organization to stage an armed assault on Congress? Who tried to assassinate President Harry Truman? Easy answer, just look up a couple of lines.
In the Twentieth Century the Puerto Rican nationalist movement was subject to draconian measures. Summary arrest and executions by colonial police of advocates for independence was common. As part of a coordinated rebellion in 1950 designed to forstall commonwealth status, two men were sent to Washington D. C. to kill the president. The Truman family was living in Blair House while the White House was being renovated. Oscar Collazo and Griselio Torresola tried to shoot their way into the presidential residence. They got as far as the steps of the house.
In 1954 the diminutive Lolita Lebron lead four Puerto Rican gunmen in a bold attack on Congress. Shouting Puerto Rico Libre! they unfurled a Puerto Rico flag and fired automatic weapons from the visitors' gallery. Five congressmen were wounded, none killed. Lebron continues to be a heroine to Puerto Rican nationalists.
Other sources: Art, Puerto Rico independence movement, FBI kills an independence leader in 2005
And So Many Others
I could keep going. The terrorism practices by union busters in the Nineteenth Century, Tim McVeigh, the many groups like the Weather Underground who blew up ROTC offices around the country during the Vietnam War, the current Minutemen. I could go on forever. In this land of the Second Amendment and a dyspeptic melting pot, terrorism fueled by race, creed, or political impotence is as American as apple pie.