Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
532 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 139 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. #81776 | C2 | semidirect |
| 2. C3×#2246 | C2 | semidirect |
| 3. #71470 | C2 | semidirect |
| 4. #71469 | C2 | semidirect |
| 5. #71461 | C2 | semidirect |
| 6. Dic3×D16 | C2 | semidirect |
| 7. #71289 | C2 | semidirect |
| 8. #69051 | C2 | semidirect |
| 9. #69045 | C2 | semidirect |
| 34. #2246 | D3 | semidirect |
| 236. C3 | #33740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81776 | 2 |
| C3×#2246 | 2 |
| #71470 | 2 |
| #71469 | 2 |
| #71461 | 2 |
| Dic3×D16 | 2 |
| #71289 | 2 |
| #69051 | 2 |
| #69045 | 2 |
| #33740 | 3 |