Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #30632315 | C2 | semidirect |
| 3. #30632056 | C2 | semidirect |
| 4. #30632047 | C2 | semidirect |
| 5. #30632042 | C2 | semidirect |
| 6. #30632038 | C2 | semidirect |
| 7. #30631697 | C2 | semidirect |
| 10. C2×#22548640 | C2 | semidirect |
| 11. #405×C251 | C2 | semidirect |
| 127. C251 | #3137 | semidirect |
| 139. #405 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632315 | 2 |
| #30632263 | 2 |
| #30632056 | 2 |
| #30632047 | 2 |
| #30632042 | 2 |
| #30632038 | 2 |
| #30631697 | 2 |
| #30631689 | 2 |
| #30631684 | 2 |
| C2×#22548640 | 2 |
| #405×C251 | 2 |
| #3137 | 251 |