Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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×#1338 | C2 | semidirect |
| 5. #67769 | C2 | semidirect |
| 6. #67559 | C2 | semidirect |
| 7. #67518 | C2 | semidirect |
| 34. #1338 | D3 | semidirect |
| 278. C3 | #11643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79958 | 2 |
| #69275 | 2 |
| #69073 | 2 |
| C3×#1338 | 2 |
| #67769 | 2 |
| #67559 | 2 |
| #67518 | 2 |
| #11643 | 3 |