Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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×#2916 | C2 | semidirect |
| 3. #72007 | C2 | semidirect |
| 4. #70723 | C2 | semidirect |
| 5. C2×#4495 | C2 | semidirect |
| 6. #70685 | C2 | semidirect |
| 13. C3×#430 | C22 | semidirect |
| 21. #4553 | C22 | semidirect |
| 23. #4494 | C22 | semidirect |
| 25. #2916 | D3 | semidirect |
| 67. #430 | C2×D3 | semidirect |
| 255. C3 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2916 | 2 |
| #83799 | 2 |
| #72007 | 2 |
| #70723 | 2 |
| C2×#4495 | 2 |
| #70685 | 2 |
| #33657 | 3 |