Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
314 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20245142 | C2 | semidirect |
| 3. #20242142 | C2 | semidirect |
| 4. #20241440 | C2 | semidirect |
| 5. #20241432 | C2 | semidirect |
| 6. #20241430 | C2 | semidirect |
| 7. C47×#1363 | C2 | semidirect |
| 150. #1363 | D47 | semidirect |
| 177. C47 | #11980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253960 | 2 |
| #20245142 | 2 |
| #20242142 | 2 |
| #20241440 | 2 |
| #20241432 | 2 |
| #20241430 | 2 |
| C47×#1363 | 2 |
| #11980 | 47 |