Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30632315 | C2 | semidirect |
| 3. #30631988 | C2 | semidirect |
| 4. #30631988 | C2 | semidirect |
| 5. #30631978 | C2 | semidirect |
| 6. #30631968 | C2 | semidirect |
| 7. #30631729 | C2 | semidirect |
| 8. #30631725 | C2 | semidirect |
| 11. #424×C251 | C2 | semidirect |
| 13. #22548715 | C22 | semidirect |
| 15. #22548707 | C22 | semidirect |
| 26. #22548649 | C22 | semidirect |
| 27. #22548649 | C22 | semidirect |
| 28. #22548649 | C22 | semidirect |
| 29. #22548647 | C22 | semidirect |
| 30. #22548647 | C22 | semidirect |
| 31. #22548647 | C22 | semidirect |
| 39. C4⋊C8×C251 | C22 | semidirect |
| 40. C4⋊C8×C251 | C22 | semidirect |
| 45. C2×D1004 | Q8 | semidirect |
| 124. C251 | #3081 | semidirect |
| 134. #424 | D251 | semidirect |
| 160. C4⋊C8 | C2×D251 | semidirect |
| 161. C4⋊C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632315 | 2 |
| #30632161 | 2 |
| #30631988 | 2 |
| #30631978 | 2 |
| #30631968 | 2 |
| #30631729 | 2 |
| #30631725 | 2 |
| #30631693 | 2 |
| C2×#22548637 | 2 |
| #424×C251 | 2 |
| #3081 | 251 |