Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #30632242 | C2 | semidirect |
| 3. #30632027 | C2 | semidirect |
| 4. #30631983 | C2 | semidirect |
| 5. #30631977 | C2 | semidirect |
| 6. #30631894 | C2 | semidirect |
| 8. #30631791 | C2 | semidirect |
| 9. #30631788 | C2 | semidirect |
| 10. #30631743 | C2 | semidirect |
| 11. #461×C251 | C2 | semidirect |
| 136. C251 | #3116 | semidirect |
| 144. #461 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| C4×#16860809 | 2 |
| #30632027 | 2 |
| #30631983 | 2 |
| #30631977 | 2 |
| #30631894 | 2 |
| #30631846 | 2 |
| #30631791 | 2 |
| #30631788 | 2 |
| #30631743 | 2 |
| #461×C251 | 2 |
| #3116 | 251 |