Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
490 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 4. #20241901 | C2 | semidirect |
| 5. #20241899 | C2 | semidirect |
| 6. #20241282 | C2 | semidirect |
| 7. C47×#1300 | C2 | semidirect |
| 10. #15689483 | C4 | semidirect |
| 11. #15689483 | C4 | semidirect |
| 34. #13094024 | C2×C4 | semidirect |
| 35. #13094024 | C2×C4 | semidirect |
| 72. #97×C47 | C2×C4 | semidirect |
| 204. #1300 | D47 | semidirect |
| 234. C47 | #9439 | semidirect |
| 271. #97 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253775 | 2 |
| #20246498 | 2 |
| #20242011 | 2 |
| #20241901 | 2 |
| #20241899 | 2 |
| #20241282 | 2 |
| C47×#1300 | 2 |
| #9439 | 47 |