Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20246498 | C2 | semidirect |
| 3. #20242011 | C2 | semidirect |
| 4. #20241897 | C2 | semidirect |
| 5. #20241895 | C2 | semidirect |
| 6. #20241282 | C2 | semidirect |
| 7. C47×#1300 | C2 | semidirect |
| 12. #15689517 | C4 | semidirect |
| 13. #15689512 | C4 | semidirect |
| 43. #13094024 | C2×C4 | semidirect |
| 44. #13094021 | C2×C4 | semidirect |
| 76. #97×C47 | C2×C4 | semidirect |
| 226. #1300 | D47 | semidirect |
| 257. C47 | #9441 | semidirect |
| 298. #97 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253854 | 2 |
| #20246498 | 2 |
| #20242011 | 2 |
| #20241897 | 2 |
| #20241895 | 2 |
| #20241282 | 2 |
| C47×#1300 | 2 |
| #9441 | 47 |