Oh yes, it is possible and quite easy. Look at the base of the plant, where it meets the soil. You'll see that the plant is made up of several clusters of stalks, each of these clusters being capable of standing on their own as a plant. If you want to divide it, simply remove the plant from the pot and gently tease the clusters apart into clumps the size you desire, taking care to leave as many roots intact as possible. Replant into fresh medium, at the same depth it was originally growing. Water well and fertilize a week later.

If this is an absolutely treasured plant, why not just repot it into a larger container and let it become a magnificently huge specimen? That way, you run little to zip risk of losing it. Good luck to you.