Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#16860799 | C2 | semidirect |
| 2. #30632258 | C2 | semidirect |
| 4. #30631933 | C2 | semidirect |
| 5. #30631916 | C2 | semidirect |
| 6. #30631725 | C2 | semidirect |
| 7. #30631697 | C2 | semidirect |
| 8. #30631693 | C2 | semidirect |
| 9. C2×#131×C251 | C2 | semidirect |
| 20. #22548694 | C22 | semidirect |
| 25. #22548649 | C22 | semidirect |
| 26. #22548647 | C22 | semidirect |
| 27. #22548640 | C22 | semidirect |
| 32. C2×M16×C251 | C22 | semidirect |
| 34. C22×C8×C251 | C22 | semidirect |
| 67. C2×C8×C251 | D4 | semidirect |
| 120. C251 | #3057 | semidirect |
| 123. C2×#131 | D251 | semidirect |
| 139. C2×M16 | C2×D251 | semidirect |
| 141. C22×C8 | C2×D251 | semidirect |
| 179. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860799 | 2 |
| #30632258 | 2 |
| #30632251 | 2 |
| #30631933 | 2 |
| #30631916 | 2 |
| #30631725 | 2 |
| #30631697 | 2 |
| #30631693 | 2 |
| C2×#131×C251 | 2 |
| #3057 | 251 |