Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22548722 | C2 | semidirect |
| 3. #30632265 | C2 | semidirect |
| 4. #30631935 | C2 | semidirect |
| 5. #30631931 | C2 | semidirect |
| 6. #30631926 | C2 | semidirect |
| 7. #30631921 | C2 | semidirect |
| 8. C2×#22548648 | C2 | semidirect |
| 9. #30631688 | C2 | semidirect |
| 10. #30631686 | C2 | semidirect |
| 11. #537×C251 | C2 | semidirect |
| 58. C2×C251⋊C8 | D4 | semidirect |
| 152. C251 | #3061 | semidirect |
| 157. #537 | 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×#22548722 | 2 |
| #30632265 | 2 |
| #30631935 | 2 |
| #30631931 | 2 |
| #30631926 | 2 |
| #30631921 | 2 |
| C2×#22548648 | 2 |
| #30631688 | 2 |
| #30631686 | 2 |
| #537×C251 | 2 |
| #3061 | 251 |