Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 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. #20244306 | C2 | semidirect |
| 3. #20241986 | C2 | semidirect |
| 4. #20241934 | C2 | semidirect |
| 5. #20241252 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#2337 | C2 | semidirect |
| 9. #15689513 | C4 | semidirect |
| 10. #15689482 | C4 | semidirect |
| 35. #13094024 | C2×C4 | semidirect |
| 36. #13094021 | C2×C4 | semidirect |
| 52. #13093935 | C2×C4 | semidirect |
| 216. #2337 | D47 | semidirect |
| 252. C47 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254375 | 2 |
| #20244306 | 2 |
| #20241986 | 2 |
| #20241934 | 2 |
| #20241252 | 2 |
| #20241244 | 2 |
| C47×#2337 | 2 |
| #9381 | 47 |