Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20242004 | C2 | semidirect |
| 5. #20241810 | C2 | semidirect |
| 6. #20241286 | C2 | semidirect |
| 7. C47×#1291 | C2 | semidirect |
| 183. #1291 | D47 | semidirect |
| 212. C47 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253551 | 2 |
| #20252040 | 2 |
| #20242004 | 2 |
| #20241820 | 2 |
| #20241810 | 2 |
| #20241286 | 2 |
| C47×#1291 | 2 |
| #9314 | 47 |