Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
394 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20243425 | C2 | semidirect |
| 4. #20241407 | C2 | semidirect |
| 5. #20241405 | C2 | semidirect |
| 6. #20241403 | C2 | semidirect |
| 7. C47×#1349 | C2 | semidirect |
| 178. #1349 | D47 | semidirect |
| 205. C47 | #11894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252967 | 2 |
| #20244997 | 2 |
| #20243425 | 2 |
| #20241407 | 2 |
| #20241405 | 2 |
| #20241403 | 2 |
| C47×#1349 | 2 |
| #11894 | 47 |