The Dwarves, they mostly live within their mountains while a wealthy but small percentage of them own land on the surface. They are very isolationist preferring not to take sides when conflict arises unless it directly affects them. The Hierarchy of the society in question is as follows:
- The Tsar - He is the sole ruler of his vast underground empire. The position is passed on to the oldest son when the Tsar dies.
- The Council - A council which makes decisions on matters beneath the Tsar and consists of a single appointed noble from each of the clans.
- The Nobility - Wealthy clans of varying power and size that have held power for many generations. The most powerful clans swearing direct fealty to the Tsar while the smaller clans swear fealty to the various greater clans. What makes them a part of the nobility is the fact that they're clan has a seat on the council and able to cast votes on decisions.
- The Boyars - wealthy non-nobles who own some mines and land but don't hold much power themselves and have only had their power for one or two generations along with nobles who've lost their seat on the council.
- The Merchants and Tradesman - The ones who own businesses and work in accordance with the Boyars.
- The Common Folk - The ones who work the land and mines for the Boyars and nobility.
The group of extremists in question wants to get rid of the nobility and the Tsar while also taking control of the mines and owning the land on the surface, and after achieving these goals they also plan to invade the surface and expand the Dwarven people beyond their mountainous homeland to greater territory on the surface. The tech level is around late 16th century with some technology of the Dwarves being ahead in some regards with the beginning emergence of snap lock muskets. The humans on the surface however only have tech equal around the end of the 14th century due to slower development on their part and also due to the Dwarves restricting trade and knowledge of their technology with them. How could a group of extremists overthrow and drastically reform such a society?
EDIT: More information because there has been a question on how this group is extremist.
The extremists are a group which is very anti-Nobility and want the people, the common folk, to own the mines and land they work and not be merely content with their lives. They also believe that the dwarven race as a whole is superior to the humans and even the elves because of their technological advancements. They believe that the nobility is holding back their people's true potential and by being rid of them they can then usher in a new age of progress for their people by invading the surface and establishing dominance upon the world above.
EDIT: To Clear up some confusion over my use of the term "Boyar" and what differentiates them from the regular nobility. Summarised, The nobility have seats on the council and the Boyar don't, Among the Boyar are disgraced nobles who've lost their seat and thus are no longer considered nobles by the other nobles, and there are also families who've only owned land or a mine for one or two generations and don't have a council seat. Additionally, if a Boyar gains enough influence they may be able to petition for their family to have a council seat, which would make them nobility, and the nobles may decide to have a vote on whether or not they may have a seat. The Tsar may also grant a council seat to a Boyar for whatever reason he wishes. Votes on the council are settled on a 6 to 10 majority basis.