Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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. #30632411 | C2 | semidirect |
| 2. #30632398 | C2 | semidirect |
| 3. #30632043 | C2 | semidirect |
| 4. #30631996 | C2 | semidirect |
| 5. #30631974 | C2 | semidirect |
| 7. #30631889 | C2 | semidirect |
| 8. C8×Dic502 | C2 | semidirect |
| 9. #30631772 | C2 | semidirect |
| 11. #487×C251 | C2 | semidirect |
| 120. C251 | #3360 | semidirect |
| 125. #487 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632411 | 2 |
| #30632398 | 2 |
| #30632043 | 2 |
| #30631996 | 2 |
| #30631974 | 2 |
| #30631905 | 2 |
| #30631889 | 2 |
| C8×Dic502 | 2 |
| #30631772 | 2 |
| C4×D2008 | 2 |
| #487×C251 | 2 |
| #3360 | 251 |