Lillies with 18 petals ?!

Hi all
I'm fairly a novice gardener but for the last 3 years I've taken a love into all types of lillium/lillies. The white ones in the photo I'd originally planted the bulbs 3 years ago. Removing from the soil/compost every year during winter and then re potting. Most of my bulbs this year were huge and have multiplied. Some to 4 times the original size. Should I be dividing the bulb every year or is this normal after 3 years growth as they only started with the standard 6 petals in the first year.
Thanks again Lauren
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Lauren