I have a problem that I have been stuck on for two hours. I would like to check if I have made any progress or I am just going in circles.

**Problem: Let be group homomorphisms. Which is larger, ?**

**My work:**

divides $|G|$ and $|H|$

divides $|G|$ and $|K|$

With similar analysis, I get .

This seems like too much work with zero output.