Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30632035 | C2 | semidirect |
| 3. #30631974 | C2 | semidirect |
| 4. #30631887 | C2 | semidirect |
| 5. Q8×C251⋊C8 | C2 | semidirect |
| 6. C4×#16860797 | C2 | semidirect |
| 7. Q82×C251 | C2 | semidirect |
| 54. Q8×C251 | SD16 | semidirect |
| 55. Q8×C251 | #41 | semidirect |
| 76. C251 | #3362 | semidirect |
| 78. Q82 | D251 | semidirect |
| 123. Q8 | #16860797 | semidirect |
| 124. Q8 | #16860811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632359 | 2 |
| #30632035 | 2 |
| #30631974 | 2 |
| #30631887 | 2 |
| Q8×C251⋊C8 | 2 |
| C4×#16860797 | 2 |
| Q82×C251 | 2 |
| #3362 | 251 |