Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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×C3×#368 | C2 | semidirect |
| 3. C2×#4502 | C2 | semidirect |
| 4. #70696 | C2 | semidirect |
| 5. C2×#4497 | C2 | semidirect |
| 14. C2×Dic24 | C4 | semidirect |
| 17. C2×#800 | C4 | semidirect |
| 18. C2×D48 | C4 | semidirect |
| 23. C2×#368 | D3 | semidirect |
| 243. C3 | #13242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4904 | 2 |
| C2×C3×#368 | 2 |
| C2×#4502 | 2 |
| #70696 | 2 |
| C2×#4497 | 2 |
| #13242 | 3 |