Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2968 | C2 | semidirect |
| 3. #71756 | C2 | semidirect |
| 4. #70790 | C2 | semidirect |
| 5. #69798 | C2 | semidirect |
| 6. #67742 | C2 | semidirect |
| 7. #67659 | C2 | semidirect |
| 19. #5067 | C4 | semidirect |
| 20. #5064 | C4 | semidirect |
| 21. #5058 | C4 | semidirect |
| 22. #5055 | C4 | semidirect |
| 37. #2968 | D3 | semidirect |
| 409. C3 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2968 | 2 |
| #83137 | 2 |
| #71756 | 2 |
| #70790 | 2 |
| #69798 | 2 |
| #67742 | 2 |
| #67659 | 2 |
| #9432 | 3 |