Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #30632222 | C2 | semidirect |
| 2. #30632071 | C2 | semidirect |
| 3. #30632044 | C2 | semidirect |
| 4. #30631929 | C2 | semidirect |
| 6. #30631917 | C2 | semidirect |
| 7. #30631781 | C2 | semidirect |
| 8. #30631774 | C2 | semidirect |
| 9. #30631769 | C2 | semidirect |
| 10. C4×C8×D251 | C2 | semidirect |
| 11. #499×C251 | C2 | semidirect |
| 118. C251 | #3168 | semidirect |
| 121. #499 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632222 | 2 |
| #30632071 | 2 |
| #30632044 | 2 |
| #30631929 | 2 |
| #30631924 | 2 |
| #30631917 | 2 |
| #30631781 | 2 |
| #30631774 | 2 |
| #30631769 | 2 |
| C4×C8×D251 | 2 |
| #499×C251 | 2 |
| #3168 | 251 |