Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #71838 | C2 | semidirect |
| 4. #69766 | C2 | semidirect |
| 5. #69726 | C2 | semidirect |
| 10. C3×#487 | C4 | semidirect |
| 11. C3×#486 | C4 | semidirect |
| 58. #487 | Dic3 | semidirect |
| 59. #486 | Dic3 | semidirect |
| 253. C3 | #9758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3131 | 2 |
| #71838 | 2 |
| #71814 | 2 |
| #69766 | 2 |
| #69726 | 2 |
| #9758 | 3 |