Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #30632423 | C2 | semidirect |
| 2. #30632394 | C2 | semidirect |
| 3. #30632040 | C2 | semidirect |
| 4. #30632033 | C2 | semidirect |
| 5. #30631985 | C2 | semidirect |
| 6. #30631983 | C2 | semidirect |
| 7. #30631900 | C2 | semidirect |
| 8. #30631811 | C2 | semidirect |
| 9. C4×#16860798 | C2 | semidirect |
| 10. D8×Dic251 | C2 | semidirect |
| 122. C251 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632423 | 2 |
| #30632394 | 2 |
| #30632040 | 2 |
| #30632033 | 2 |
| #30631985 | 2 |
| #30631983 | 2 |
| #30631900 | 2 |
| #30631811 | 2 |
| C4×#16860798 | 2 |
| D8×Dic251 | 2 |
| #459×C251 | 2 |
| #3361 | 251 |