Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. #30632063 | C2 | semidirect |
| 2. #30631882 | C2 | semidirect |
| 3. #30631765 | C2 | semidirect |
| 4. #30631437 | C2 | semidirect |
| 5. #30631431 | C2 | semidirect |
| 6. #30631430 | C2 | semidirect |
| 7. #459×C251 | C2 | semidirect |
| 53. C251⋊C8 | D8 | semidirect |
| 92. C251 | #1687 | semidirect |
| 96. #459 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632063 | 2 |
| #30631882 | 2 |
| #30631765 | 2 |
| #30631437 | 2 |
| #30631431 | 2 |
| #30631430 | 2 |
| #459×C251 | 2 |
| #1687 | 251 |