Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #30632083 | C2 | semidirect |
| 4. #30632030 | C2 | semidirect |
| 5. #30632016 | C2 | semidirect |
| 6. #30631973 | C2 | semidirect |
| 7. #30631944 | C2 | semidirect |
| 8. C4×#16860800 | C2 | semidirect |
| 10. #30631728 | C2 | semidirect |
| 11. #477×C251 | C2 | semidirect |
| 116. C251 | #3356 | semidirect |
| 123. #477 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632410 | 2 |
| #30632398 | 2 |
| #30632083 | 2 |
| #30632030 | 2 |
| #30632016 | 2 |
| #30631973 | 2 |
| #30631944 | 2 |
| C4×#16860800 | 2 |
| #30631764 | 2 |
| #30631728 | 2 |
| #477×C251 | 2 |
| #3356 | 251 |