Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2967 | C2 | semidirect |
| 3. #71757 | C2 | semidirect |
| 4. #70835 | C2 | semidirect |
| 5. #69853 | C2 | semidirect |
| 6. #67757 | C2 | semidirect |
| 7. #67666 | C2 | semidirect |
| 19. #5069 | C4 | semidirect |
| 20. #5067 | C4 | semidirect |
| 21. #5060 | C4 | semidirect |
| 22. #5058 | C4 | semidirect |
| 37. #2967 | D3 | semidirect |
| 402. C3 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2967 | 2 |
| #83147 | 2 |
| #71757 | 2 |
| #70835 | 2 |
| #69853 | 2 |
| #67757 | 2 |
| #67666 | 2 |
| #9370 | 3 |