Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #30632487 | C2 | semidirect |
| 2. C2×#22548741 | C2 | semidirect |
| 3. C2×#22548741 | C2 | semidirect |
| 4. #30632453 | C2 | semidirect |
| 5. #30631956 | C2 | semidirect |
| 6. #30631949 | C2 | semidirect |
| 7. #30631735 | C2 | semidirect |
| 8. #30631669 | C2 | semidirect |
| 9. C2×#100×C251 | C2 | semidirect |
| 13. #22548748 | C22 | semidirect |
| 15. #22548743 | C22 | semidirect |
| 22. C2×#16860798 | C22 | semidirect |
| 24. C2×#16860795 | C22 | semidirect |
| 25. #22548723 | C22 | semidirect |
| 30. #22548650 | C22 | semidirect |
| 31. #22548633 | C22 | semidirect |
| 32. #22548631 | C22 | semidirect |
| 36. #100×C251 | C22 | semidirect |
| 147. C251 | #3068 | semidirect |
| 157. C2×#100 | D251 | semidirect |
| 184. #100 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632487 | 2 |
| C2×#22548741 | 2 |
| #30632453 | 2 |
| #30631956 | 2 |
| #30631949 | 2 |
| #30631735 | 2 |
| #30631669 | 2 |
| C2×#100×C251 | 2 |
| #3068 | 251 |