Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20242105 | C2 | semidirect |
| 5. #20241245 | C2 | semidirect |
| 6. #20241243 | C2 | semidirect |
| 7. C47×#1556 | C2 | semidirect |
| 188. #1556 | D47 | semidirect |
| 220. C47 | #9453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252416 | 2 |
| #20248562 | 2 |
| #20242105 | 2 |
| #20241728 | 2 |
| #20241245 | 2 |
| #20241243 | 2 |
| C47×#1556 | 2 |
| #9453 | 47 |