Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20241965 | C2 | semidirect |
| 3. #20241936 | C2 | semidirect |
| 4. #20241806 | C2 | semidirect |
| 5. #20241253 | C2 | semidirect |
| 6. #20241251 | C2 | semidirect |
| 7. C47×#2967 | C2 | semidirect |
| 9. #15689518 | C4 | semidirect |
| 10. #15689513 | C4 | semidirect |
| 11. #15689493 | C4 | semidirect |
| 12. #15689489 | C4 | semidirect |
| 200. #2967 | D47 | semidirect |
| 239. C47 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254421 | 2 |
| #20241965 | 2 |
| #20241936 | 2 |
| #20241806 | 2 |
| #20241253 | 2 |
| #20241251 | 2 |
| C47×#2967 | 2 |
| #9370 | 47 |