There are two main options.
- Because electrons can’t be made from smaller things, there isn’t anything to “split into”. This is what the Standard Model claims and all evidence is consistent with it. It’s possible, however, that…
- Electrons are made from things that are so tightly held together that even the most powerful particle accelerators cannot get them to move.
We can still learn about the sub-structure of things by hitting them hard and observing how much energy is transferred to make the internal parts move relative to one another. This is because electrons don’t have the ability to split. It would require far more energy than they can provide.
Personally, I tend to lean towards #1 due to the extremely low upper bound on electron size, but it is impossible for me not to favor #2.