Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #30632218 | C2 | semidirect |
| 2. #30632088 | C2 | semidirect |
| 3. #30632070 | C2 | semidirect |
| 4. #30632040 | C2 | semidirect |
| 5. #30631928 | C2 | semidirect |
| 6. #30631914 | C2 | semidirect |
| 7. #30631781 | C2 | semidirect |
| 8. #30631778 | C2 | semidirect |
| 9. D8×Dic251 | C2 | semidirect |
| 10. C2×C8×Dic251 | C2 | semidirect |
| 118. C251 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632218 | 2 |
| #30632088 | 2 |
| #30632070 | 2 |
| #30632040 | 2 |
| #30631928 | 2 |
| #30631914 | 2 |
| #30631781 | 2 |
| #30631778 | 2 |
| D8×Dic251 | 2 |
| C2×C8×Dic251 | 2 |
| #466×C251 | 2 |
| #3168 | 251 |