Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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×#3216 | C2 | semidirect |
| 2. #83338 | C2 | semidirect |
| 4. #71827 | C2 | semidirect |
| 5. #71801 | C2 | semidirect |
| 6. #70828 | C2 | semidirect |
| 7. #67754 | C2 | semidirect |
| 34. #3216 | D3 | semidirect |
| 384. C3 | #10124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3216 | 2 |
| #83338 | 2 |
| #83306 | 2 |
| #71827 | 2 |
| #71801 | 2 |
| #70828 | 2 |
| #67754 | 2 |
| #10124 | 3 |