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. #30632031 | C2 | semidirect |
| 4. #30631964 | C2 | semidirect |
| 5. #30631897 | C2 | semidirect |
| 6. #30631893 | C2 | semidirect |
| 8. #30631779 | C2 | semidirect |
| 9. #30631774 | C2 | semidirect |
| 10. #30631739 | C2 | semidirect |
| 11. #475×C251 | C2 | semidirect |
| 136. C251 | #3107 | semidirect |
| 141. #475 | 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 |
| #30632031 | 2 |
| #30631964 | 2 |
| #30631897 | 2 |
| #30631893 | 2 |
| #30631852 | 2 |
| #30631779 | 2 |
| #30631774 | 2 |
| #30631739 | 2 |
| #475×C251 | 2 |
| #3107 | 251 |