Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
314 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20255992 | C2 | semidirect |
| 2. #20245420 | C2 | semidirect |
| 3. #20242864 | C2 | semidirect |
| 4. #20241440 | C2 | semidirect |
| 5. #20241356 | C2 | semidirect |
| 6. #20241347 | C2 | semidirect |
| 7. C47×#2244 | C2 | semidirect |
| 148. #2244 | D47 | semidirect |
| 179. C47 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255992 | 2 |
| #20245420 | 2 |
| #20242864 | 2 |
| #20241440 | 2 |
| #20241356 | 2 |
| #20241347 | 2 |
| C47×#2244 | 2 |
| #12348 | 47 |