Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 8. C3×#500 | C4 | semidirect |
| 9. C3×#494 | C4 | semidirect |
| 10. C3×#487 | C4 | semidirect |
| 53. #500 | Dic3 | semidirect |
| 54. #494 | Dic3 | semidirect |
| 55. #487 | Dic3 | semidirect |
| 91. C4×Dic3 | Q16 | semidirect |
| 228. C3 | #9845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3170 | 2 |
| #71839 | 2 |
| #71826 | 2 |
| C4×C8×Dic3 | 2 |
| #69731 | 2 |
| #9845 | 3 |