Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 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×#2995 | C2 | semidirect |
| 3. #71754 | C2 | semidirect |
| 4. #70801 | C2 | semidirect |
| 5. #70513 | C2 | semidirect |
| 6. #67748 | C2 | semidirect |
| 7. #67710 | C2 | semidirect |
| 21. #5067 | C4 | semidirect |
| 22. #5064 | C4 | semidirect |
| 23. #5058 | C4 | semidirect |
| 24. #5055 | C4 | semidirect |
| 37. #2995 | D3 | semidirect |
| 424. C3 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2995 | 2 |
| #83135 | 2 |
| #71754 | 2 |
| #70801 | 2 |
| #70513 | 2 |
| #67748 | 2 |
| #67710 | 2 |
| #8997 | 3 |