Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1102 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 351 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. C3×#2916 | C2 | semidirect |
| 3. #83780 | C2 | semidirect |
| 4. C2×#4496 | C2 | semidirect |
| 5. #70687 | C2 | semidirect |
| 23. #2916 | D3 | semidirect |
| 222. C3 | #33393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5753 | 2 |
| C3×#2916 | 2 |
| #83780 | 2 |
| C2×#4496 | 2 |
| #70687 | 2 |
| #33393 | 3 |