Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1469 | C2 | semidirect |
| 3. #71718 | C2 | semidirect |
| 4. #70804 | C2 | semidirect |
| 5. #70794 | C2 | semidirect |
| 6. #70784 | C2 | semidirect |
| 7. #70741 | C2 | semidirect |
| 37. #1469 | D3 | semidirect |
| 398. C3 | #9791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5059 | 2 |
| C3×#1469 | 2 |
| #71718 | 2 |
| #70804 | 2 |
| #70794 | 2 |
| #70784 | 2 |
| #70741 | 2 |
| #9791 | 3 |