Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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. C22×Dic1004 | C2 | semidirect |
| 3. #30632343 | C2 | semidirect |
| 4. #30632070 | C2 | semidirect |
| 5. #30631929 | C2 | semidirect |
| 6. #30631908 | C2 | semidirect |
| 7. #30631850 | C2 | semidirect |
| 8. #30631825 | C2 | semidirect |
| 9. #30631781 | C2 | semidirect |
| 10. C8×C22⋊D251 | C2 | semidirect |
| 11. #466×C251 | C2 | semidirect |
| 55. Dic1004 | D4 | semidirect |
| 116. C22×C251 | #135 | semidirect |
| 136. C251 | #3285 | semidirect |
| 143. #466 | D251 | semidirect |
| 256. C22 | #22548734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548734 | 2 |
| C22×Dic1004 | 2 |
| #30632343 | 2 |
| #30632070 | 2 |
| #30631929 | 2 |
| #30631908 | 2 |
| #30631850 | 2 |
| #30631825 | 2 |
| #30631781 | 2 |
| C8×C22⋊D251 | 2 |
| #466×C251 | 2 |
| #3285 | 251 |