Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632410 | C2 | semidirect |
| 2. #30632397 | C2 | semidirect |
| 3. #30632042 | C2 | semidirect |
| 4. #30632038 | C2 | semidirect |
| 5. #30631995 | C2 | semidirect |
| 6. #30631978 | C2 | semidirect |
| 8. #30631893 | C2 | semidirect |
| 9. C4×#16860799 | C2 | semidirect |
| 11. C8×Q8×C251 | C2 | semidirect |
| 120. C251 | #3360 | semidirect |
| 130. C8×Q8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632410 | 2 |
| #30632397 | 2 |
| #30632042 | 2 |
| #30632038 | 2 |
| #30631995 | 2 |
| #30631978 | 2 |
| #30631903 | 2 |
| #30631893 | 2 |
| C4×#16860799 | 2 |
| C4×D2008 | 2 |
| C8×Q8×C251 | 2 |
| #3360 | 251 |