Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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. #30632407 | C2 | semidirect |
| 2. #30632090 | C2 | semidirect |
| 3. #30632022 | C2 | semidirect |
| 4. #30632008 | C2 | semidirect |
| 5. #30631969 | C2 | semidirect |
| 6. #30631967 | C2 | semidirect |
| 7. #30631931 | C2 | semidirect |
| 8. C4×#16860798 | C2 | semidirect |
| 9. #30631765 | C2 | semidirect |
| 10. #30631727 | C2 | semidirect |
| 82. C251⋊C8 | #41 | semidirect |
| 122. C251 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632407 | 2 |
| #30632090 | 2 |
| #30632022 | 2 |
| #30632008 | 2 |
| #30631969 | 2 |
| #30631967 | 2 |
| #30631931 | 2 |
| C4×#16860798 | 2 |
| #30631765 | 2 |
| #30631727 | 2 |
| #547×C251 | 2 |
| #3353 | 251 |