Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#22548646 | C2 | semidirect |
| 3. C2×#22548640 | C2 | semidirect |
| 4. C2×C8×Dic251 | C2 | semidirect |
| 5. #30631592 | C2 | semidirect |
| 11. C2×#16860798 | C4 | semidirect |
| 67. C2×Dic251 | SD16 | semidirect |
| 68. C251⋊C8 | C22⋊C4 | semidirect |
| 112. C251 | #1968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860798 | 2 |
| C2×#22548646 | 2 |
| C2×#22548640 | 2 |
| C2×C8×Dic251 | 2 |
| #30631592 | 2 |
| #30631590 | 2 |
| C2×#102×C251 | 2 |
| #1968 | 251 |