Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20252442 | C2 | semidirect |
| 3. #20241893 | C2 | semidirect |
| 4. C2×#15688857 | C2 | semidirect |
| 5. #20241275 | C2 | semidirect |
| 6. #20241230 | C2 | semidirect |
| 7. C47×#1471 | C2 | semidirect |
| 9. #15689458 | C4 | semidirect |
| 11. #15689441 | C4 | semidirect |
| 14. #15689274 | C4 | semidirect |
| 16. #15689257 | C4 | semidirect |
| 240. #1471 | D47 | semidirect |
| 280. C47 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254153 | 2 |
| #20252442 | 2 |
| #20241893 | 2 |
| C2×#15688857 | 2 |
| #20241275 | 2 |
| #20241230 | 2 |
| C47×#1471 | 2 |
| #9264 | 47 |