This again is a very successful way to produce new plants and is quicker at producing mature specimens than leaf cuttings.
Remove your plant from its pot as detailed in the propagation - division section. When you have identified a good strong rhizome/root, cut it into at least 2.5cm lengths and soak each piece in a fungicide solution or Trichoderma solution for around 10 minutes.
Using a pot of ideally milled spagnum moss or your usual compost, lay the cuttings out horizontally and cover to a depth of 5-10mm with either the same compost or, as I prefer, the milled spagnum moss. Keep in a shaded, warm - around 68F, humid - 75% position. New growth appears usually within 2-4 weeks.
In my experience planting the cuttings vertically in the pot seems to produce more but smaller leaves compared to planting horizontally which produces fewer but larger leaves and earlier pitchers.