Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 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. #30632064 | C2 | semidirect |
| 2. #30631882 | C2 | semidirect |
| 3. #30631440 | C2 | semidirect |
| 4. #30631430 | C2 | semidirect |
| 5. C8×D4×C251 | C2 | semidirect |
| 42. D4×C251 | D8 | semidirect |
| 51. C8×C251 | D8 | semidirect |
| 70. C251 | #1667 | semidirect |
| 74. C8×D4 | D251 | semidirect |
| 112. D4 | D2008 | semidirect |
| 122. C8 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632064 | 2 |
| #30631882 | 2 |
| #30631440 | 2 |
| #30631430 | 2 |
| C8×D4×C251 | 2 |
| #1667 | 251 |