Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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. #30631741 | C2 | semidirect |
| 3. #30631532 | C2 | semidirect |
| 4. #30631422 | C2 | semidirect |
| 5. #30631421 | C2 | semidirect |
| 6. #30631420 | C2 | semidirect |
| 7. #327×C251 | C2 | semidirect |
| 9. #22548714 | C4 | semidirect |
| 10. #22548711 | C4 | semidirect |
| 14. D4×Dic251 | C4 | semidirect |
| 15. #22548677 | C4 | semidirect |
| 119. C251 | #1505 | semidirect |
| 127. #327 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632232 | 2 |
| #30631741 | 2 |
| #30631532 | 2 |
| #30631422 | 2 |
| #30631421 | 2 |
| #30631420 | 2 |
| #327×C251 | 2 |
| #1505 | 251 |