Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#22548734 | C2 | semidirect |
| 2. C2×#22548721 | C2 | semidirect |
| 3. #30632266 | C2 | semidirect |
| 4. #30631932 | C2 | semidirect |
| 5. #30631931 | C2 | semidirect |
| 6. #30631929 | C2 | semidirect |
| 7. #30631928 | C2 | semidirect |
| 8. #30631920 | C2 | semidirect |
| 9. #107×D251 | C2 | semidirect |
| 10. #30631685 | C2 | semidirect |
| 11. #466×C251 | C2 | semidirect |
| 64. C8×D251 | D4 | semidirect |
| 143. C251 | #3061 | semidirect |
| 153. #466 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548734 | 2 |
| C2×#22548721 | 2 |
| #30632266 | 2 |
| #30631932 | 2 |
| #30631931 | 2 |
| #30631929 | 2 |
| #30631928 | 2 |
| #30631920 | 2 |
| #107×D251 | 2 |
| #30631685 | 2 |
| #466×C251 | 2 |
| #3061 | 251 |