Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #20254129 | C2 | semidirect |
| 4. #20243051 | C2 | semidirect |
| 5. #20243046 | C2 | semidirect |
| 6. #20243045 | C2 | semidirect |
| 7. #20243001 | C2 | semidirect |
| 8. #20241691 | C2 | semidirect |
| 9. C47×#3185 | C2 | semidirect |
| 12. #15689519 | C22 | semidirect |
| 13. #15689502 | C22 | semidirect |
| 16. #15689475 | C22 | semidirect |
| 17. #15689473 | C22 | semidirect |
| 29. #15688845 | C22 | semidirect |
| 30. #15688844 | C22 | semidirect |
| 31. C8×C47⋊C8 | C22 | semidirect |
| 33. C47×#498 | C22 | semidirect |
| 34. C47×#494 | C22 | semidirect |
| 35. C47×#487 | C22 | semidirect |
| 157. #3185 | D47 | semidirect |
| 173. #498 | C2×D47 | semidirect |
| 175. #494 | C2×D47 | semidirect |
| 180. #487 | C2×D47 | semidirect |
| 198. C47 | #19753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254129 | 2 |
| #20253764 | 2 |
| #20253763 | 2 |
| #20243051 | 2 |
| #20243046 | 2 |
| #20243045 | 2 |
| #20243001 | 2 |
| #20241691 | 2 |
| C47×#3185 | 2 |
| #19753 | 47 |