Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
378 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 378 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. #79578 | C2 | semidirect |
| 2. C3×#2206 | C2 | semidirect |
| 3. #71290 | C2 | semidirect |
| 4. #71286 | C2 | semidirect |
| 5. #67763 | C2 | semidirect |
| 6. #67560 | C2 | semidirect |
| 7. #67558 | C2 | semidirect |
| 28. #2206 | D3 | semidirect |
| 172. Dic6 | D16 | semidirect |
| 290. C3 | #12328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79578 | 2 |
| C3×#2206 | 2 |
| #71290 | 2 |
| #71286 | 2 |
| #67763 | 2 |
| #67560 | 2 |
| #67558 | 2 |
| #12328 | 3 |