Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1545 | C2 | semidirect |
| 3. #71759 | C2 | semidirect |
| 4. #70756 | C2 | semidirect |
| 5. #70750 | C2 | semidirect |
| 6. #70527 | C2 | semidirect |
| 7. #67714 | C2 | semidirect |
| 30. #1545 | D3 | semidirect |
| 359. C3 | #10440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5072 | 2 |
| C3×#1545 | 2 |
| #71759 | 2 |
| #70756 | 2 |
| #70750 | 2 |
| #70527 | 2 |
| #67714 | 2 |
| #10440 | 3 |