Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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. #20242026 | C2 | semidirect |
| 3. #20241939 | C2 | semidirect |
| 5. #20241260 | C2 | semidirect |
| 6. #20241253 | C2 | semidirect |
| 20. C47×#500 | C4 | semidirect |
| 21. C47×#492 | C4 | semidirect |
| 22. C47×#487 | C4 | semidirect |
| 23. C47×#486 | C4 | semidirect |
| 169. #500 | Dic47 | semidirect |
| 170. #492 | Dic47 | semidirect |
| 171. #487 | Dic47 | semidirect |
| 172. #486 | Dic47 | semidirect |
| 186. C47 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252459 | 2 |
| #20242026 | 2 |
| #20241939 | 2 |
| #20241935 | 2 |
| #20241260 | 2 |
| #20241253 | 2 |
| C47×#3182 | 2 |
| #9415 | 47 |