Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20241882 | C2 | semidirect |
| 4. #20241677 | C2 | semidirect |
| 5. C4×#106×C47 | C2 | semidirect |
| 7. #15689528 | C4 | semidirect |
| 8. #15689500 | C4 | semidirect |
| 9. #15689470 | C4 | semidirect |
| 117. C8×C47 | #104 | semidirect |
| 139. C4×#106 | D47 | semidirect |
| 165. C47 | #9721 | semidirect |
| 261. C8 | #13093952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253967 | 2 |
| #20244306 | 2 |
| #20241882 | 2 |
| #20241677 | 2 |
| C4×#106×C47 | 2 |
| #9721 | 47 |