Im not too sure they can be divided in the same way as say, herbaceous or grasses can be but cuttings are taken instead.

Im sure that all that top growth comes from a single stem which can get quite woody in older plants.

I stand to be corrected as im not a dianthus expert

Yes they grow from a single stem, the best way is to take cuttings but it is a bit late now, I always take mine in early summer.