Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 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. #30632412 | C2 | semidirect |
| 3. #30632036 | C2 | semidirect |
| 4. #30631970 | C2 | semidirect |
| 5. #30631969 | C2 | semidirect |
| 8. C8×Dic502 | C2 | semidirect |
| 11. #487×C251 | C2 | semidirect |
| 78. Dic502 | SD16 | semidirect |
| 118. C251 | #3359 | semidirect |
| 123. #487 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632412 | 2 |
| #30632352 | 2 |
| #30632036 | 2 |
| #30631970 | 2 |
| #30631969 | 2 |
| #30631891 | 2 |
| #30631889 | 2 |
| C8×Dic502 | 2 |
| C4×#16860799 | 2 |
| #30631772 | 2 |
| #487×C251 | 2 |
| #3359 | 251 |