Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. #30632407 | C2 | semidirect |
| 2. #30632394 | C2 | semidirect |
| 3. #30632040 | C2 | semidirect |
| 4. #30632038 | C2 | semidirect |
| 5. #30631993 | C2 | semidirect |
| 6. #30631977 | C2 | semidirect |
| 8. #30631892 | C2 | semidirect |
| 9. C8×Dic502 | C2 | semidirect |
| 10. #30631778 | C2 | semidirect |
| 120. C251 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632407 | 2 |
| #30632394 | 2 |
| #30632040 | 2 |
| #30632038 | 2 |
| #30631993 | 2 |
| #30631977 | 2 |
| #30631900 | 2 |
| #30631892 | 2 |
| C8×Dic502 | 2 |
| #30631778 | 2 |
| C4×D8×C251 | 2 |
| #3360 | 251 |