Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632358 | C2 | semidirect |
| 2. #30632035 | C2 | semidirect |
| 3. #30632011 | C2 | semidirect |
| 4. #30631979 | C2 | semidirect |
| 5. #30631921 | C2 | semidirect |
| 6. #30631882 | C2 | semidirect |
| 7. #30631830 | C2 | semidirect |
| 8. C4×#16860798 | C2 | semidirect |
| 9. D4×C251⋊C8 | C2 | semidirect |
| 10. #30631681 | C2 | semidirect |
| 11. #555×C251 | C2 | semidirect |
| 132. C251 | #3305 | semidirect |
| 134. #555 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632358 | 2 |
| #30632035 | 2 |
| #30632011 | 2 |
| #30631979 | 2 |
| #30631921 | 2 |
| #30631882 | 2 |
| #30631830 | 2 |
| C4×#16860798 | 2 |
| D4×C251⋊C8 | 2 |
| #30631681 | 2 |
| #555×C251 | 2 |
| #3305 | 251 |