Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 4. #20241983 | C2 | semidirect |
| 5. #20241281 | C2 | semidirect |
| 6. #20241261 | C2 | semidirect |
| 7. C47×#1506 | C2 | semidirect |
| 10. #15689415 | C4 | semidirect |
| 11. #15689410 | C4 | semidirect |
| 12. #15689330 | C4 | semidirect |
| 13. #15689325 | C4 | semidirect |
| 194. #1506 | D47 | semidirect |
| 227. C47 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253544 | 2 |
| #20252400 | 2 |
| #20243199 | 2 |
| #20241983 | 2 |
| #20241281 | 2 |
| #20241261 | 2 |
| C47×#1506 | 2 |
| #9159 | 47 |