Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C3×#1707 | C2 | semidirect |
| 5. #67801 | C2 | semidirect |
| 6. #67793 | C2 | semidirect |
| 7. #67439 | C2 | semidirect |
| 26. #1707 | D3 | semidirect |
| 212. C3 | #12422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1707 | 2 |
| #71387 | 2 |
| #71315 | 2 |
| C8×D24 | 2 |
| #67801 | 2 |
| #67793 | 2 |
| #67439 | 2 |
| #12422 | 3 |