Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #30631996 | C2 | semidirect |
| 4. #30631990 | C2 | semidirect |
| 5. #30631974 | C2 | semidirect |
| 6. #30631972 | C2 | semidirect |
| 7. #30631968 | C2 | semidirect |
| 8. #30631724 | C2 | semidirect |
| 9. C4⋊C8×D251 | C2 | semidirect |
| 11. #477×C251 | C2 | semidirect |
| 44. #16860811 | Q8 | semidirect |
| 134. C251 | #3076 | semidirect |
| 140. #477 | 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 |
| #30631996 | 2 |
| #30631990 | 2 |
| #30631974 | 2 |
| #30631972 | 2 |
| #30631968 | 2 |
| #30631724 | 2 |
| C4⋊C8×D251 | 2 |
| #30631682 | 2 |
| #477×C251 | 2 |
| #3076 | 251 |