There are many types of crinum (just one "i") lilies with different needs (amount of sun/shade, moisture requirements, etc) and different behaviors. Generally, species crinums are much less likely to multiply vegetatively (by offsets) than hybrids. The crinums you see, that quickly turn into clumps, are very likely hybrids. Most species crinums are best propagated by seed. Crinums are not dioecious.

thanks for the info!
Lori

If I had to guess (and I do), I'd say your Crinum is a species, most likely bulbispermum or macowanii. Both of these, however, should set lots of viable seed, since that's their main method of reproduction. Many species Crinums do offset heavily (americanum, erubescens, oliganthemum, and scabrum, to name a few), but it is true that most hybrids will produce offsets rather than seeds.

In his book "Garden Bulbs for the South" Scott Ogden says to plant crinums bulbs deeply (12-18 inches down; pg 191) so that they do not off set too freely. Perhaps your crinum is set too deep?
Susan.