Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #30631645 | C2 | semidirect |
| 5. C2×#22548625 | C2 | semidirect |
| 6. #30631448 | C2 | semidirect |
| 7. #341×C251 | C2 | semidirect |
| 10. #22548723 | C4 | semidirect |
| 16. #22548641 | C4 | semidirect |
| 17. #22548640 | C4 | semidirect |
| 18. #22548637 | C4 | semidirect |
| 98. C251 | #1765 | semidirect |
| 105. #341 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548723 | 2 |
| C2×#22548641 | 2 |
| #30631684 | 2 |
| #30631645 | 2 |
| C2×#22548625 | 2 |
| #30631448 | 2 |
| #341×C251 | 2 |
| #1765 | 251 |