I've had good luck with the back to back spading fork method, but have heard of people who have broken forks. Anyway if you want to try it you put two spading forks back to back in the center of the clump--you may well have to stand on them to get them in--and then push the handles apart and you should end up with two smaller clumps. I also use a large screwdriver stuck into spaces between roots and just wiggle it around until something separates. Good luck.
Val

Search on YouTube. There are several videos about dividing daylilies.