Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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. #30631436 | C2 | semidirect |
| 5. #30631435 | C2 | semidirect |
| 6. #30631435 | C2 | semidirect |
| 7. #333×C251 | C2 | semidirect |
| 88. C251 | #1548 | semidirect |
| 96. #333 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D251 | 2 |
| #30631739 | 2 |
| #30631709 | 2 |
| #30631436 | 2 |
| #30631435 | 2 |
| #333×C251 | 2 |
| #1548 | 251 |