In your case, seems as if you allowed the pups grow up next to the parent plant. Instead of seperating one, you want to seperate them all, and remove the main corm.

That shouldn't be a problem at all. One way to go about it is to remove it from it's bucket, and give it a good spraying down to remove the dirt. Once the dirt is cleared away you'll have a better idea of what you're working with.

Then just seperate the plants with a sharp knife. One note in this process, if a pup plant is very small, and doesn't have it's own root system yet, you will have to cut into the main corm abit. Cut a peace of the main corm when you cut the small plants out and they'll do fine.

Now for the main corm, once it's out you got options. This is something I read about and will try this spring.

Corm division.

What I read is that the main corm will have "eye's" on it like a canna rhyzome. And that I can divide the corm with each piece having an eye and make even more plants.

EIther, good luck and happy gardening!