Its better to divide them now then later. They need time to root in. Just get a very sharp knife and cut them in half or quarters depending on how big the bunch is.
I found this link it should help.

Here is a link that might be useful: planting daylilies

Dig the whole clump out of the ground and shake the soil off the roots. Then look down into it and you will see that what you have is lots of small plants that are growing right next door to each other. Use your knife to cut between each little plant, without cutting anymore roots than you have to. Or you can leave about 3 little plants in each piece so that you have bigger clumps. The ones on the outside of the clump are usually younger and more vigorous. Replant those. The center is often getting woody and worn out. Throw it away. Be sure to plant them in good, fertile, loose soil. Set the crown of the plant at ground level, and water well. Definitely add a good mulch before your temperatures get too cold.

Black eyed Susans are a good plant to learn on. You will have to work really hard to hurt it. Killing it is nearly impossible. I actually dug up a big clump of "herbstonne" in the spring and had to use a pruning saw to cut it into pieces. It never even wilted. Really. You can do it. :)

Early spring (1st couple of weeks of April) is a better time to divide in our zone.
But now works. Early spring you don't have to worry about them making it thru winter, and there is still enough time for them to settle in and bloom. Especially for plants that bloom July on... Good luck.....mark

Thank you. I will have to try this. Although I am afraid I will not dig deep enough and shallow cut the roots. The soil is hard here.

Your soil should be loosened down to one foot (a spade's depth). This is best done in the soil prep phase, but can be done at any time. If your soil is not loose that far down, the vast majority of the plant's roots will be sitting on top of the hard soil. So, you should be able to get them up by pushing the spade down as far as it will go. YOu will always break some roots when you dig or divide, but the plants are very forgiving. When you re-plant the clumps, loosen the soil deeper and work in some organic matter, at least in the holes. Dig the holes nice and wide (2 to 3 feet in diameter).

To make the soil easier to work with, I would suggest watering it really well the day before you do the digging, so that it's slightly cool and barely moist when you work it. Don't dig into really wet soil, though, because it will get too compact when you transplant, which will compound your problem. And, I agree that you'll want to add some organic matter (mushroom compost or peat, in a ratio of about 2 parts soil to one part compost) to a big hole around where you're putting the new plants, so that over time your soil texture improves...doesn't hurt to put a nice layer of compost over the top of the soil in your garden every year, for the same reason (ie, to improve the soil texture).