Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C3×#1997 | C2 | semidirect |
| 3. #71779 | C2 | semidirect |
| 6. #69850 | C2 | semidirect |
| 7. #67715 | C2 | semidirect |
| 31. #1997 | D3 | semidirect |
| 356. C3 | #10502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83216 | 2 |
| C3×#1997 | 2 |
| #71779 | 2 |
| #70503 | 2 |
| #69867 | 2 |
| #69850 | 2 |
| #67715 | 2 |
| #10502 | 3 |