Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. C2×#22548625 | C2 | semidirect |
| 5. #30631583 | C2 | semidirect |
| 6. #30631449 | C2 | semidirect |
| 7. #340×C251 | C2 | semidirect |
| 15. #22548637 | C4 | semidirect |
| 118. C251 | #1936 | semidirect |
| 126. #340 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548637 | 2 |
| C2×#22548635 | 2 |
| C2×#22548625 | 2 |
| #30631588 | 2 |
| #30631583 | 2 |
| #30631449 | 2 |
| #340×C251 | 2 |
| #1936 | 251 |