Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
376 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 73 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. #69119 | C2 | semidirect |
| 3. #68710 | C2 | semidirect |
| 4. C3×#1339 | C2 | semidirect |
| 5. #67778 | C2 | semidirect |
| 6. #67536 | C2 | semidirect |
| 7. #67482 | C2 | semidirect |
| 9. C2×#912 | C4 | semidirect |
| 13. #5159 | C4 | semidirect |
| 19. #4867 | C4 | semidirect |
| 20. D3×#106 | C4 | semidirect |
| 34. #1339 | D3 | semidirect |
| 360. C3 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #80866 | 2 |
| #69119 | 2 |
| #68710 | 2 |
| C3×#1339 | 2 |
| #67778 | 2 |
| #67536 | 2 |
| #67482 | 2 |
| #11867 | 3 |