Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 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×#22548631 | C2 | semidirect |
| 5. #568×C251 | C2 | semidirect |
| 13. C2×#16860794 | C22 | semidirect |
| 14. #22548633 | C22 | semidirect |
| 15. #22548631 | C22 | semidirect |
| 18. C2×M16×C251 | C22 | semidirect |
| 76. C251 | #2888 | semidirect |
| 80. #568 | D251 | semidirect |
| 93. C2×M16 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548761 | 2 |
| #30632454 | 2 |
| #30631669 | 2 |
| C2×#22548631 | 2 |
| #568×C251 | 2 |
| #2888 | 251 |