Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 2. #83133 | C2 | semidirect |
| 3. C3×#1500 | C2 | semidirect |
| 4. #70765 | C2 | semidirect |
| 5. #69440 | C2 | semidirect |
| 6. #67743 | C2 | semidirect |
| 7. #67615 | C2 | semidirect |
| 13. #5067 | C4 | semidirect |
| 14. #5064 | C4 | semidirect |
| 15. #5058 | C4 | semidirect |
| 16. #5055 | C4 | semidirect |
| 39. #1500 | 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 |
|---|---|
| #83135 | 2 |
| #83133 | 2 |
| C3×#1500 | 2 |
| #70765 | 2 |
| #69440 | 2 |
| #67743 | 2 |
| #67615 | 2 |
| #8997 | 3 |