Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
566 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×C3×#364 | C2 | semidirect |
| 3. C2×#4516 | C2 | semidirect |
| 4. #71440 | C2 | semidirect |
| 5. #69779 | C2 | semidirect |
| 16. #4695 | C4 | semidirect |
| 22. C2×#364 | D3 | semidirect |
| 51. #819 | D4 | semidirect |
| 52. #818 | D4 | semidirect |
| 257. C3 | #13261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4695 | 2 |
| C2×C3×#364 | 2 |
| C2×#4516 | 2 |
| #71440 | 2 |
| #69779 | 2 |
| #13261 | 3 |