Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 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. #20241998 | C2 | semidirect |
| 3. #20241949 | C2 | semidirect |
| 4. #20241926 | C2 | semidirect |
| 5. #20241288 | C2 | semidirect |
| 6. #20241270 | C2 | semidirect |
| 7. C47×#2968 | C2 | semidirect |
| 9. #15689533 | C4 | semidirect |
| 10. #15689513 | C4 | semidirect |
| 11. #15689489 | C4 | semidirect |
| 12. #15689482 | C4 | semidirect |
| 203. #2968 | D47 | semidirect |
| 243. C47 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254087 | 2 |
| #20241998 | 2 |
| #20241949 | 2 |
| #20241926 | 2 |
| #20241288 | 2 |
| #20241270 | 2 |
| C47×#2968 | 2 |
| #9432 | 47 |