Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20244997 | C2 | semidirect |
| 3. #341×D47 | C2 | semidirect |
| 4. #20241406 | C2 | semidirect |
| 5. #20241404 | C2 | semidirect |
| 6. #20241402 | C2 | semidirect |
| 7. C47×#1350 | C2 | semidirect |
| 179. #1350 | D47 | semidirect |
| 208. C47 | #11710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252971 | 2 |
| #20244997 | 2 |
| #341×D47 | 2 |
| #20241406 | 2 |
| #20241404 | 2 |
| #20241402 | 2 |
| C47×#1350 | 2 |
| #11710 | 47 |