Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 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 |
|---|---|---|
| 2. #30631480 | C2 | semidirect |
| 3. #353×C251 | C2 | semidirect |
| 6. #22548712 | C4 | semidirect |
| 8. C4×C251⋊C8 | C4 | semidirect |
| 52. C251 | #1408 | semidirect |
| 56. #353 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632063 | 2 |
| #30631480 | 2 |
| #353×C251 | 2 |
| #1408 | 251 |