Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
380 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×#1569 | C2 | semidirect |
| 4. #70510 | C2 | semidirect |
| 5. #69862 | C2 | semidirect |
| 7. #67753 | C2 | semidirect |
| 34. #1569 | D3 | semidirect |
| 355. C3 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79351 | 2 |
| C3×#1569 | 2 |
| #70523 | 2 |
| #70510 | 2 |
| #69862 | 2 |
| #69860 | 2 |
| #67753 | 2 |
| #10498 | 3 |