Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
338 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #20242153 | C2 | semidirect |
| 5. #20241287 | C2 | semidirect |
| 6. #20241277 | C2 | semidirect |
| 7. C47×#1838 | C2 | semidirect |
| 162. #1838 | D47 | semidirect |
| 196. C47 | #8917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252555 | 2 |
| #20242153 | 2 |
| #20241974 | 2 |
| #20241851 | 2 |
| #20241287 | 2 |
| #20241277 | 2 |
| C47×#1838 | 2 |
| #8917 | 47 |