Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632221 | C2 | semidirect |
| 2. #30632093 | C2 | semidirect |
| 3. #30632074 | C2 | semidirect |
| 4. #30632051 | C2 | semidirect |
| 5. #30632049 | C2 | semidirect |
| 6. #30631938 | C2 | semidirect |
| 7. #30631931 | C2 | semidirect |
| 8. C4×#16860798 | C2 | semidirect |
| 9. C4×#16860795 | C2 | semidirect |
| 10. C4×#16860794 | C2 | semidirect |
| 11. #532×C251 | C2 | semidirect |
| 91. C251⋊C8 | #41 | semidirect |
| 137. C251 | #3171 | semidirect |
| 139. #532 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632221 | 2 |
| #30632093 | 2 |
| #30632074 | 2 |
| #30632051 | 2 |
| #30632049 | 2 |
| #30631938 | 2 |
| #30631931 | 2 |
| C4×#16860798 | 2 |
| C4×#16860795 | 2 |
| C4×#16860794 | 2 |
| #532×C251 | 2 |
| #3171 | 251 |