Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #30632412 | C2 | semidirect |
| 3. #30632040 | C2 | semidirect |
| 4. #30631985 | C2 | semidirect |
| 5. #30631969 | C2 | semidirect |
| 6. #30631908 | C2 | semidirect |
| 8. C8×Dic502 | C2 | semidirect |
| 9. C4×Dic1004 | C2 | semidirect |
| 10. #30631778 | C2 | semidirect |
| 117. C251 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632423 | 2 |
| #30632412 | 2 |
| #30632040 | 2 |
| #30631985 | 2 |
| #30631969 | 2 |
| #30631908 | 2 |
| #30631884 | 2 |
| C8×Dic502 | 2 |
| C4×Dic1004 | 2 |
| #30631778 | 2 |
| #486×C251 | 2 |
| #3365 | 251 |