Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #20245675 | C2 | semidirect |
| 2. #20245525 | C2 | semidirect |
| 3. #20242911 | C2 | semidirect |
| 4. #20241440 | C2 | semidirect |
| 5. #20241355 | C2 | semidirect |
| 6. #20241346 | C2 | semidirect |
| 167. C47 | #12400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245675 | 2 |
| #20245525 | 2 |
| #20242911 | 2 |
| #20241440 | 2 |
| #20241355 | 2 |
| #20241346 | 2 |
| C47×#3355 | 2 |
| #12400 | 47 |