Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 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. #30632244 | C2 | semidirect |
| 3. #30631988 | C2 | semidirect |
| 4. #30631978 | C2 | semidirect |
| 5. #30631968 | C2 | semidirect |
| 6. #30631729 | C2 | semidirect |
| 8. #423×C251 | C2 | semidirect |
| 11. #22548715 | C22 | semidirect |
| 12. #22548715 | C22 | semidirect |
| 13. #22548707 | C22 | semidirect |
| 25. #22548649 | C22 | semidirect |
| 26. #22548647 | C22 | semidirect |
| 31. C4⋊C8×C251 | C22 | semidirect |
| 32. C4⋊C8×C251 | C22 | semidirect |
| 38. C2×D1004 | Q8 | semidirect |
| 115. C251 | #3077 | semidirect |
| 123. #423 | D251 | semidirect |
| 145. C4⋊C8 | C2×D251 | semidirect |
| 146. C4⋊C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632244 | 2 |
| C2×C4×D1004 | 2 |
| #30631988 | 2 |
| #30631978 | 2 |
| #30631968 | 2 |
| #30631729 | 2 |
| #30631693 | 2 |
| #423×C251 | 2 |
| #3077 | 251 |