Mark, I'll second Ashley's ID as A. cyathophorum var. farreri... the narrow stems and red stem bases are a giveaway, as is the general aspect of the plant and seed.
To divide, gentle tease the slender "bulb bases" apart, they should separate... the bulbs are nothing more than slightly thickened stem bases with some white fleshy roots. Sometimes two stems are attached and can't be separated, but you should be able to get a fair number of divisions.
PS: Allium aflatunense (note spelling) is one of the tall spring-blooming summer-dormant "big ball" onions, or as Richadd Dadd called them, cricket ball onions. By the way, does anyone know how Richard Dadd is doing, I haven't heard from him in a long time.