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. #30631997 | C2 | semidirect |
| 4. #30631989 | C2 | semidirect |
| 5. #30631979 | C2 | semidirect |
| 6. #30631973 | C2 | semidirect |
| 7. #30631967 | C2 | semidirect |
| 8. #30631722 | C2 | semidirect |
| 9. C4⋊C8×D251 | C2 | semidirect |
| 11. #476×C251 | C2 | semidirect |
| 44. #16860809 | Q8 | semidirect |
| 134. C251 | #3076 | semidirect |
| 141. #476 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| C4×#16860809 | 2 |
| #30631997 | 2 |
| #30631989 | 2 |
| #30631979 | 2 |
| #30631973 | 2 |
| #30631967 | 2 |
| #30631722 | 2 |
| C4⋊C8×D251 | 2 |
| #30631680 | 2 |
| #476×C251 | 2 |
| #3076 | 251 |