Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 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. #20241371 | C2 | semidirect |
| 5. #20241370 | C2 | semidirect |
| 6. #20241369 | C2 | semidirect |
| 7. C47×#1338 | C2 | semidirect |
| 144. #1338 | D47 | semidirect |
| 168. C47 | #11643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252319 | 2 |
| #20245190 | 2 |
| #20245189 | 2 |
| #20241371 | 2 |
| #20241370 | 2 |
| #20241369 | 2 |
| C47×#1338 | 2 |
| #11643 | 47 |