Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22548735 | C2 | semidirect |
| 2. C2×#22548723 | C2 | semidirect |
| 3. #30632268 | C2 | semidirect |
| 4. #30632265 | C2 | semidirect |
| 5. #30631936 | C2 | semidirect |
| 6. #30631932 | C2 | semidirect |
| 7. #30631927 | C2 | semidirect |
| 8. #30631922 | C2 | semidirect |
| 9. C2×#22548648 | C2 | semidirect |
| 10. #30631689 | C2 | semidirect |
| 11. #417×C251 | C2 | semidirect |
| 63. C2×C251⋊C8 | D4 | semidirect |
| 152. C251 | #3061 | semidirect |
| 164. #417 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548735 | 2 |
| C2×#22548723 | 2 |
| #30632268 | 2 |
| #30632265 | 2 |
| #30631936 | 2 |
| #30631932 | 2 |
| #30631927 | 2 |
| #30631922 | 2 |
| C2×#22548648 | 2 |
| #30631689 | 2 |
| #417×C251 | 2 |
| #3061 | 251 |