Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #30632023 | C2 | semidirect |
| 4. #30631968 | C2 | semidirect |
| 5. #30631893 | C2 | semidirect |
| 7. #30631789 | C2 | semidirect |
| 8. #432×C251 | C2 | semidirect |
| 12. #22548715 | C22 | semidirect |
| 13. #22548715 | C22 | semidirect |
| 18. C4×Dic502 | C22 | semidirect |
| 26. #22548649 | C22 | semidirect |
| 27. #22548640 | C22 | semidirect |
| 30. C4⋊C8×C251 | C22 | semidirect |
| 32. #97×C251 | C22 | semidirect |
| 112. C251 | #3110 | semidirect |
| 121. #432 | D251 | semidirect |
| 141. C4⋊C8 | C2×D251 | semidirect |
| 145. #97 | 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 |
| #30632023 | 2 |
| #30631968 | 2 |
| #30631893 | 2 |
| #30631840 | 2 |
| #30631789 | 2 |
| #432×C251 | 2 |
| #3110 | 251 |