Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
314 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 67 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. #79742 | C2 | semidirect |
| 2. C3×#2207 | C2 | semidirect |
| 3. #71288 | C2 | semidirect |
| 5. #67765 | C2 | semidirect |
| 6. #67565 | C2 | semidirect |
| 7. #67556 | C2 | semidirect |
| 28. #2207 | D3 | semidirect |
| 156. D12 | SD32 | semidirect |
| 263. C3 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79742 | 2 |
| C3×#2207 | 2 |
| #71288 | 2 |
| #71282 | 2 |
| #67765 | 2 |
| #67565 | 2 |
| #67556 | 2 |
| #12342 | 3 |