Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
880 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 263 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. #83910 | C2 | semidirect |
| 3. #72086 | C2 | semidirect |
| 4. #71817 | C2 | semidirect |
| 5. #69829 | C2 | semidirect |
| 10. C3×#497 | C4 | semidirect |
| 11. C3×#496 | C4 | semidirect |
| 48. #819 | D4 | semidirect |
| 56. #497 | Dic3 | semidirect |
| 57. #496 | Dic3 | semidirect |
| 220. C3 | #23197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3150 | 2 |
| #83910 | 2 |
| #72086 | 2 |
| #71817 | 2 |
| #69829 | 2 |
| #23197 | 3 |