Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 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. #20252518 | C2 | semidirect |
| 3. C4×#13093952 | C2 | semidirect |
| 4. #20241805 | C2 | semidirect |
| 5. #20241277 | C2 | semidirect |
| 6. #20241221 | C2 | semidirect |
| 7. C47×#1962 | C2 | semidirect |
| 10. #15689415 | C4 | semidirect |
| 11. #15689410 | C4 | semidirect |
| 12. #15689320 | C4 | semidirect |
| 13. #15689315 | C4 | semidirect |
| 179. Dic94 | #104 | semidirect |
| 213. #1962 | D47 | semidirect |
| 249. C47 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253442 | 2 |
| #20252518 | 2 |
| C4×#13093952 | 2 |
| #20241805 | 2 |
| #20241277 | 2 |
| #20241221 | 2 |
| C47×#1962 | 2 |
| #8970 | 47 |