The Executor’s sublights are called Executor-50.x engines, and that’s about all we know. I couldn’t even tell you for sure what kind of engine they are. However, KDY also manufactured the Imperial I-class and Victory I-class Star Destroyers, which both use ion engines for sublight travel. I think it’s safe to assume that the Executor-50.x engines are also ion drives, albeit massive ones. Since I can’t give you specifics on the engines, I’ll give you a rundown of how ion drives work.
Ion drives use a controlled fusion reaction to produce a stream of charged particles, which are forced out of the exhaust ports to provide thrust. These particles are mildly radioactive (in the case of the Executor, any ship that flew too close to the engines would be vaporized by the radiation) and they travel at close to the speed of light. The engines can be powered by generators, chemical reactants, power cells, or pretty much any other sufficient source of power. On Executor-class Star Dreadnoughts, power came from one main reactor and a number of secondary reactors, though the type of reactor is unknown. If the engines are indeed ion drives, they will be nuclear fusion reactors cores.
That’s about everything I can find, unfortunately. I hope it helped!
~ Jacen