Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 95 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×#1946 | C2 | semidirect |
| 3. #70687 | C2 | semidirect |
| 4. #70656 | C2 | semidirect |
| 5. #67663 | C2 | semidirect |
| 24. #1946 | D3 | semidirect |
| 51. C3×#106 | D4 | semidirect |
| 137. #106 | D12 | semidirect |
| 259. C3 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78499 | 2 |
| C3×#1946 | 2 |
| #70687 | 2 |
| #70656 | 2 |
| #67663 | 2 |
| #13416 | 3 |