Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #30631972 | C2 | semidirect |
| 5. #30631968 | C2 | semidirect |
| 6. #30631889 | C2 | semidirect |
| 8. Q16×Dic251 | C2 | semidirect |
| 9. #30631772 | C2 | semidirect |
| 10. #30631739 | C2 | semidirect |
| 11. #462×C251 | C2 | semidirect |
| 136. C251 | #3107 | semidirect |
| 143. #462 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| C4×#16860811 | 2 |
| #30632027 | 2 |
| #30631972 | 2 |
| #30631968 | 2 |
| #30631889 | 2 |
| #30631848 | 2 |
| Q16×Dic251 | 2 |
| #30631772 | 2 |
| #30631739 | 2 |
| #462×C251 | 2 |
| #3107 | 251 |