Date: Thu, 20 Aug 1992 13:51 EDT
From: hoey@aic.nrl.navy.mil

[...]

Of course a list of *all*
the subgroups would have, um, over three beelion of them. I suspect
it has more than 4.3x10^19. Does anyone know a good way of counting
how many subgroups there are? Or even a way of estimating the number?
By comparison, the symmetries of the cube form a 48-element group with
98 subgroups.

All we should really be interested in are conjugate classes of
subgroups. I think.