Let h and k be subgroups of a group g. if g = hk and g = hk, where h eh and k ek, is there any relationship among lgl, lhi, and ik1? what if g = h x k?

Let H and K be subgroups of a group G. If G = HK and g = hk, where h EH and k EK, is there any relationship among lgl, lhi, and Ik1? What if G = H x K?