Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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×#1525 | C2 | semidirect |
| 3. #71801 | C2 | semidirect |
| 4. C4×#822 | C2 | semidirect |
| 5. #69859 | C2 | semidirect |
| 6. #69853 | C2 | semidirect |
| 7. #69847 | C2 | semidirect |
| 35. #1525 | D3 | semidirect |
| 360. C3 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83291 | 2 |
| C3×#1525 | 2 |
| #71801 | 2 |
| C4×#822 | 2 |
| #69859 | 2 |
| #69853 | 2 |
| #69847 | 2 |
| #9726 | 3 |