Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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×#22548737 | C2 | semidirect |
| 3. C2×#22548721 | C2 | semidirect |
| 4. #30631963 | C2 | semidirect |
| 5. #30631958 | C2 | semidirect |
| 6. #30631951 | C2 | semidirect |
| 7. #30631669 | C2 | semidirect |
| 8. C2×#108×C251 | C2 | semidirect |
| 20. C2×Dic1004 | C22 | semidirect |
| 21. C2×#16860799 | C22 | semidirect |
| 22. C2×D2008 | C22 | semidirect |
| 30. #22548633 | C22 | semidirect |
| 31. #22548631 | C22 | semidirect |
| 34. #108×C251 | C22 | semidirect |
| 35. #108×C251 | C22 | semidirect |
| 132. C251 | #3067 | semidirect |
| 140. C2×#108 | D251 | semidirect |
| 165. #108 | C2×D251 | semidirect |
| 166. #108 | 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×#22548737 | 2 |
| C2×#22548721 | 2 |
| #30631963 | 2 |
| #30631958 | 2 |
| #30631951 | 2 |
| #30631669 | 2 |
| C2×#108×C251 | 2 |
| #3067 | 251 |