Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
212 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 79 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×#2170 | C2 | semidirect |
| 3. #69056 | C2 | semidirect |
| 4. #67766 | C2 | semidirect |
| 5. #67568 | C2 | semidirect |
| 6. #67566 | C2 | semidirect |
| 7. #67498 | C2 | semidirect |
| 26. #2170 | D3 | semidirect |
| 43. #829 | C8 | semidirect |
| 44. #828 | C8 | semidirect |
| 45. #827 | C8 | semidirect |
| 46. #826 | C8 | semidirect |
| 200. C3 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2170 | 2 |
| #70921 | 2 |
| #69056 | 2 |
| #67766 | 2 |
| #67568 | 2 |
| #67566 | 2 |
| #67498 | 2 |
| #12047 | 3 |