Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
464 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20252450 | C2 | semidirect |
| 3. #20241916 | C2 | semidirect |
| 4. #20241747 | C2 | semidirect |
| 5. #20241296 | C2 | semidirect |
| 6. #20241265 | C2 | semidirect |
| 7. C47×#1516 | C2 | semidirect |
| 9. #15689451 | C4 | semidirect |
| 11. #15689434 | C4 | semidirect |
| 14. #15689273 | C4 | semidirect |
| 16. #15689256 | C4 | semidirect |
| 220. #1516 | D47 | semidirect |
| 260. C47 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254198 | 2 |
| #20252450 | 2 |
| #20241916 | 2 |
| #20241747 | 2 |
| #20241296 | 2 |
| #20241265 | 2 |
| C47×#1516 | 2 |
| #9332 | 47 |