Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #30632090 | C2 | semidirect |
| 3. #30632025 | C2 | semidirect |
| 4. #30632000 | C2 | semidirect |
| 5. #30631982 | C2 | semidirect |
| 6. #30631974 | C2 | semidirect |
| 7. #30631935 | C2 | semidirect |
| 8. C4×#16860797 | C2 | semidirect |
| 9. #30631765 | C2 | semidirect |
| 10. #30631727 | C2 | semidirect |
| 11. #554×C251 | C2 | semidirect |
| 121. C251 | #3357 | semidirect |
| 124. #554 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632402 | 2 |
| #30632090 | 2 |
| #30632025 | 2 |
| #30632000 | 2 |
| #30631982 | 2 |
| #30631974 | 2 |
| #30631935 | 2 |
| C4×#16860797 | 2 |
| #30631765 | 2 |
| #30631727 | 2 |
| #554×C251 | 2 |
| #3357 | 251 |