Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30632061 | C2 | semidirect |
| 3. D4×C251⋊C8 | C2 | semidirect |
| 4. #30631437 | C2 | semidirect |
| 5. #30631433 | C2 | semidirect |
| 6. #30631430 | C2 | semidirect |
| 7. #474×C251 | C2 | semidirect |
| 52. C251⋊C8 | D8 | semidirect |
| 57. D4×C251 | SD16 | semidirect |
| 85. C251 | #1665 | semidirect |
| 88. #474 | D251 | semidirect |
| 139. D4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632061 | 2 |
| #30631882 | 2 |
| D4×C251⋊C8 | 2 |
| #30631437 | 2 |
| #30631433 | 2 |
| #30631430 | 2 |
| #474×C251 | 2 |
| #1665 | 251 |