Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. #70787 | C2 | semidirect |
| 4. #69863 | C2 | semidirect |
| 6. C3×#1283 | C2 | semidirect |
| 7. #67708 | C2 | semidirect |
| 40. #1283 | D3 | semidirect |
| 399. C3 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79287 | 2 |
| C2×#4847 | 2 |
| #70787 | 2 |
| #69863 | 2 |
| #69855 | 2 |
| C3×#1283 | 2 |
| #67708 | 2 |
| #9245 | 3 |