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. #81909 | C2 | semidirect |
| 2. C3×#2253 | C2 | semidirect |
| 3. #71352 | C2 | semidirect |
| 4. #69348 | C2 | semidirect |
| 5. #69339 | C2 | semidirect |
| 6. #69327 | C2 | semidirect |
| 7. #69317 | C2 | semidirect |
| 8. #69060 | C2 | semidirect |
| 9. #69051 | C2 | semidirect |
| 33. #2253 | 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 |
|---|---|
| #81909 | 2 |
| C3×#2253 | 2 |
| #71352 | 2 |
| #69348 | 2 |
| #69339 | 2 |
| #69327 | 2 |
| #69317 | 2 |
| #69060 | 2 |
| #69051 | 2 |
| #33740 | 3 |