Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
358 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20245188 | C2 | semidirect |
| 3. #20243517 | C2 | semidirect |
| 4. #20241398 | C2 | semidirect |
| 5. #20241397 | C2 | semidirect |
| 6. #20241396 | C2 | semidirect |
| 7. C47×#1347 | C2 | semidirect |
| 9. #15689527 | C4 | semidirect |
| 10. #15689498 | C4 | semidirect |
| 14. D8×Dic47 | C4 | semidirect |
| 15. #15689205 | C4 | semidirect |
| 170. #1347 | D47 | semidirect |
| 197. C47 | #11858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253962 | 2 |
| #20245188 | 2 |
| #20243517 | 2 |
| #20241398 | 2 |
| #20241397 | 2 |
| #20241396 | 2 |
| C47×#1347 | 2 |
| #11858 | 47 |