Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 4. C3×#1332 | C2 | semidirect |
| 5. #67765 | C2 | semidirect |
| 6. #67505 | C2 | semidirect |
| 7. #67472 | C2 | semidirect |
| 34. #1332 | D3 | semidirect |
| 292. C3 | #11676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79725 | 2 |
| C4×#798 | 2 |
| #68570 | 2 |
| C3×#1332 | 2 |
| #67765 | 2 |
| #67505 | 2 |
| #67472 | 2 |
| #11676 | 3 |