Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
620 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 620 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. #74298 | C2 | semidirect |
| 3. C3×#1514 | C2 | semidirect |
| 4. #71813 | C2 | semidirect |
| 5. #70818 | C2 | semidirect |
| 6. #67752 | C2 | semidirect |
| 7. #67633 | C2 | semidirect |
| 14. #5085 | C4 | semidirect |
| 15. #5073 | C4 | semidirect |
| 30. #1514 | D3 | semidirect |
| 38. C3×C4⋊Q8 | C2×C4 | semidirect |
| 39. C3×#127 | C2×C4 | semidirect |
| 71. C4×C3⋊C8 | C2×C4 | semidirect |
| 145. C4⋊Q8 | C4×D3 | semidirect |
| 150. #127 | C4×D3 | semidirect |
| 356. C3 | #9428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83287 | 2 |
| #74298 | 2 |
| C3×#1514 | 2 |
| #71813 | 2 |
| #70818 | 2 |
| #67752 | 2 |
| #67633 | 2 |
| #9428 | 3 |