Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #30632243 | C2 | semidirect |
| 3. #30632057 | C2 | semidirect |
| 4. #30632056 | C2 | semidirect |
| 5. #30632051 | C2 | semidirect |
| 6. #30632045 | C2 | semidirect |
| 7. #30631680 | C2 | semidirect |
| 8. #97×D251 | C2 | semidirect |
| 9. #490×C251 | C2 | semidirect |
| 90. C251 | #3135 | semidirect |
| 97. #490 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632243 | 2 |
| #30632235 | 2 |
| #30632057 | 2 |
| #30632056 | 2 |
| #30632051 | 2 |
| #30632045 | 2 |
| #30631680 | 2 |
| #97×D251 | 2 |
| #490×C251 | 2 |
| #3135 | 251 |