Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
480 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. #79054 | C2 | semidirect |
| 3. #70818 | C2 | semidirect |
| 4. #70805 | C2 | semidirect |
| 5. #70521 | C2 | semidirect |
| 6. C3×#1307 | C2 | semidirect |
| 7. #67754 | C2 | semidirect |
| 39. #1307 | D3 | semidirect |
| 398. C3 | #9340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79353 | 2 |
| #79054 | 2 |
| #70818 | 2 |
| #70805 | 2 |
| #70521 | 2 |
| C3×#1307 | 2 |
| #67754 | 2 |
| #9340 | 3 |