Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
704 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 249 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. #30632454 | C2 | semidirect |
| 3. #30631669 | C2 | semidirect |
| 4. C2×#22548633 | C2 | semidirect |
| 5. #568×C251 | C2 | semidirect |
| 74. C251 | #2889 | semidirect |
| 78. #568 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548762 | 2 |
| #30632454 | 2 |
| #30631669 | 2 |
| C2×#22548633 | 2 |
| #568×C251 | 2 |
| #2889 | 251 |