Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22548743 | C2 | semidirect |
| 2. #30632237 | C2 | semidirect |
| 3. C2×C4×D1004 | C2 | semidirect |
| 4. #30631903 | C2 | semidirect |
| 5. #30631893 | C2 | semidirect |
| 6. #30631883 | C2 | semidirect |
| 7. #30631689 | C2 | semidirect |
| 8. #423×C251 | C2 | semidirect |
| 15. #22548715 | C22 | semidirect |
| 16. #22548712 | C22 | semidirect |
| 17. #22548703 | C22 | semidirect |
| 28. #22548640 | C22 | semidirect |
| 29. #22548637 | C22 | semidirect |
| 32. C4⋊C8×C251 | C22 | semidirect |
| 33. C4⋊C8×C251 | C22 | semidirect |
| 42. C2×D1004 | D4 | semidirect |
| 118. C4×C251 | AGL(1,ℤ/8) | semidirect |
| 129. C251 | #3036 | semidirect |
| 137. #423 | D251 | semidirect |
| 160. C4⋊C8 | C2×D251 | semidirect |
| 161. C4⋊C8 | C2×D251 | semidirect |
| 250. C4 | #22548743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548743 | 2 |
| #30632237 | 2 |
| C2×C4×D1004 | 2 |
| #30631903 | 2 |
| #30631893 | 2 |
| #30631883 | 2 |
| #30631689 | 2 |
| #423×C251 | 2 |
| #3036 | 251 |