Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#22548650 | C2 | semidirect |
| 5. #30631446 | C2 | semidirect |
| 6. #30631441 | C2 | semidirect |
| 7. #424×C251 | C2 | semidirect |
| 18. #22548638 | C4 | semidirect |
| 19. #22548638 | C4 | semidirect |
| 20. #22548635 | C4 | semidirect |
| 21. #22548635 | C4 | semidirect |
| 109. C251 | #1866 | semidirect |
| 113. #424 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548721 | 2 |
| C2×#22548650 | 2 |
| C2×#22548641 | 2 |
| #30631681 | 2 |
| #30631446 | 2 |
| #30631441 | 2 |
| #424×C251 | 2 |
| #1866 | 251 |