Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 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. #74262 | C2 | semidirect |
| 3. C3×#1514 | C2 | semidirect |
| 4. #71818 | C2 | semidirect |
| 5. #70804 | C2 | semidirect |
| 6. #67750 | C2 | semidirect |
| 7. #67633 | C2 | semidirect |
| 15. #5089 | C4 | semidirect |
| 16. #5074 | C4 | semidirect |
| 36. #1514 | D3 | semidirect |
| 43. C3×C4⋊Q8 | C2×C4 | semidirect |
| 44. C3×#127 | C2×C4 | semidirect |
| 85. #803 | C2×C4 | semidirect |
| 172. C4⋊Q8 | C4×D3 | semidirect |
| 173. #127 | C4×D3 | semidirect |
| 435. C3 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83306 | 2 |
| #74262 | 2 |
| C3×#1514 | 2 |
| #71818 | 2 |
| #70804 | 2 |
| #67750 | 2 |
| #67633 | 2 |
| #9381 | 3 |