Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #30632060 | C2 | semidirect |
| 2. #30631967 | C2 | semidirect |
| 4. #30631438 | C2 | semidirect |
| 5. #30631434 | C2 | semidirect |
| 6. #30631430 | C2 | semidirect |
| 7. C8×D4×C251 | C2 | semidirect |
| 56. D4×C251 | SD16 | semidirect |
| 65. C8×C251 | D8 | semidirect |
| 85. C251 | #1665 | semidirect |
| 90. C8×D4 | D251 | semidirect |
| 139. D4 | #16860799 | semidirect |
| 151. C8 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632060 | 2 |
| #30631967 | 2 |
| #30631882 | 2 |
| #30631438 | 2 |
| #30631434 | 2 |
| #30631430 | 2 |
| C8×D4×C251 | 2 |
| #1665 | 251 |