Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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. #30632410 | C2 | semidirect |
| 3. #30632090 | C2 | semidirect |
| 4. #30632021 | C2 | semidirect |
| 5. #30632013 | C2 | semidirect |
| 6. #30631968 | C2 | semidirect |
| 7. #30631936 | C2 | semidirect |
| 8. C4×#16860797 | C2 | semidirect |
| 9. #30631764 | C2 | semidirect |
| 10. #30631726 | C2 | semidirect |
| 11. #475×C251 | C2 | semidirect |
| 89. C251⋊C8 | #41 | semidirect |
| 122. C251 | #3353 | semidirect |
| 129. #475 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632410 | 2 |
| #30632340 | 2 |
| #30632090 | 2 |
| #30632021 | 2 |
| #30632013 | 2 |
| #30631968 | 2 |
| #30631936 | 2 |
| C4×#16860797 | 2 |
| #30631764 | 2 |
| #30631726 | 2 |
| #475×C251 | 2 |
| #3353 | 251 |