Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #30632165 | C2 | semidirect |
| 4. #30631790 | C2 | semidirect |
| 5. #30631772 | C2 | semidirect |
| 6. #30631723 | C2 | semidirect |
| 8. #30631645 | C2 | semidirect |
| 9. #419×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 16. Q8×Dic251 | C22 | semidirect |
| 23. #22548648 | C22 | semidirect |
| 24. #22548646 | C22 | semidirect |
| 26. #22548625 | C22 | semidirect |
| 27. C8×Dic251 | C22 | semidirect |
| 31. #103×C251 | C22 | semidirect |
| 38. #16860797 | C2×C4 | semidirect |
| 39. #16860797 | C2×C4 | semidirect |
| 40. C2×C251⋊C8 | C2×C4 | semidirect |
| 54. C2×Q8×C251 | C2×C4 | semidirect |
| 103. C251 | #2949 | semidirect |
| 111. #419 | D251 | semidirect |
| 132. #103 | C2×D251 | semidirect |
| 139. C2×Q8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| #30632165 | 2 |
| #30632161 | 2 |
| #30631790 | 2 |
| #30631772 | 2 |
| #30631723 | 2 |
| #30631693 | 2 |
| #30631645 | 2 |
| #419×C251 | 2 |
| #2949 | 251 |