Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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. C4×#798 | C2 | semidirect |
| 3. #68570 | C2 | semidirect |
| 4. C3×#1331 | C2 | semidirect |
| 5. #67763 | C2 | semidirect |
| 6. #67504 | C2 | semidirect |
| 7. #67471 | C2 | semidirect |
| 34. #1331 | D3 | semidirect |
| 322. C3 | #11675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79598 | 2 |
| C4×#798 | 2 |
| #68570 | 2 |
| C3×#1331 | 2 |
| #67763 | 2 |
| #67504 | 2 |
| #67471 | 2 |
| #11675 | 3 |