Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #20252527 | C2 | semidirect |
| 3. #20244315 | C2 | semidirect |
| 4. #20242101 | C2 | semidirect |
| 5. #20241257 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#1509 | C2 | semidirect |
| 9. #15689513 | C4 | semidirect |
| 10. #15689489 | C4 | semidirect |
| 213. #1509 | D47 | semidirect |
| 248. C47 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254403 | 2 |
| #20252527 | 2 |
| #20244315 | 2 |
| #20242101 | 2 |
| #20241257 | 2 |
| #20241244 | 2 |
| C47×#1509 | 2 |
| #9378 | 47 |