Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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×#22548721 | C2 | semidirect |
| 2. #30632254 | C2 | semidirect |
| 3. #30631937 | C2 | semidirect |
| 4. #30631920 | C2 | semidirect |
| 5. #30631725 | C2 | semidirect |
| 6. #30631692 | C2 | semidirect |
| 7. C22×D8×C251 | C2 | semidirect |
| 11. C2×#16860793 | C22 | semidirect |
| 12. C2×C8×D251 | C22 | semidirect |
| 15. #22548686 | C22 | semidirect |
| 18. #22548649 | C22 | semidirect |
| 19. #22548647 | C22 | semidirect |
| 20. #22548636 | C22 | semidirect |
| 49. C2×C8×C251 | D4 | semidirect |
| 93. C251 | #3058 | semidirect |
| 95. C22×D8 | D251 | semidirect |
| 139. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548721 | 2 |
| #30632254 | 2 |
| #30631937 | 2 |
| #30631920 | 2 |
| #30631725 | 2 |
| #30631692 | 2 |
| C22×D8×C251 | 2 |
| #3058 | 251 |