Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #30632242 | C2 | semidirect |
| 3. #30632021 | C2 | semidirect |
| 4. #30631968 | C2 | semidirect |
| 5. #30631967 | C2 | semidirect |
| 6. #30631889 | C2 | semidirect |
| 8. #30631790 | C2 | semidirect |
| 9. #30631788 | C2 | semidirect |
| 10. #30631743 | C2 | semidirect |
| 11. #461×C251 | C2 | semidirect |
| 15. #22548715 | C22 | semidirect |
| 19. Q8×Dic251 | C22 | semidirect |
| 30. #22548649 | C22 | semidirect |
| 31. #22548648 | C22 | semidirect |
| 32. C4⋊(C251⋊C8) | C22 | semidirect |
| 33. #22548639 | C22 | semidirect |
| 37. #22548625 | C22 | semidirect |
| 39. C4⋊Q8×C251 | C22 | semidirect |
| 41. C4⋊C8×C251 | C22 | semidirect |
| 42. #103×C251 | C22 | semidirect |
| 146. C251 | #3110 | semidirect |
| 154. #461 | D251 | semidirect |
| 164. C4⋊Q8 | C2×D251 | semidirect |
| 183. C4⋊C8 | C2×D251 | semidirect |
| 185. #103 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| C4×D4×D251 | 2 |
| #30632021 | 2 |
| #30631968 | 2 |
| #30631967 | 2 |
| #30631889 | 2 |
| #30631836 | 2 |
| #30631790 | 2 |
| #30631788 | 2 |
| #30631743 | 2 |
| #461×C251 | 2 |
| #3110 | 251 |