Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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. C2×#22548748 | C2 | semidirect |
| 3. C22×#16860799 | C2 | semidirect |
| 4. C2×#22548721 | C2 | semidirect |
| 5. #30631951 | C2 | direct (N × H) |
| 6. C2×#22548633 | C2 | semidirect |
| 7. C2×#22548631 | C2 | semidirect |
| 8. C2×#108×C251 | C2 | semidirect |
| 13. #22548748 | C22 | semidirect |
| 22. C2×#16860799 | C22 | semidirect |
| 25. #22548721 | C22 | semidirect |
| 29. #22548633 | C22 | semidirect |
| 30. #22548631 | C22 | semidirect |
| 34. #108×C251 | C22 | semidirect |
| 134. C2×C251 | #471 | semidirect |
| 138. C251 | C2×#471 | semidirect |
| 145. C2×#108 | D251 | semidirect |
| 171. #108 | C2×D251 | semidirect |
| 275. C2 | #30631951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| C2×#22548743 | 2 |
| C22×#16860799 | 2 |
| C2×#22548721 | 2 |
| #30631951 | 2 |
| C2×#22548633 | 2 |
| C2×#22548631 | 2 |
| C2×#108×C251 | 2 |
| C2×#471 | 251 |