Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
782 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#4716 | C2 | semidirect |
| 4. C3×#1838 | C2 | semidirect |
| 5. #70528 | C2 | semidirect |
| 6. #68949 | C2 | semidirect |
| 7. #68944 | C2 | semidirect |
| 8. #68922 | C2 | semidirect |
| 37. #1838 | D3 | semidirect |
| 308. C3 | #28179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79067 | 2 |
| C2×#4716 | 2 |
| #78491 | 2 |
| C3×#1838 | 2 |
| #70528 | 2 |
| #68949 | 2 |
| #68944 | 2 |
| #68922 | 2 |
| #28179 | 3 |