Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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×#4717 | C2 | semidirect |
| 3. C3×#1975 | C2 | semidirect |
| 4. #72080 | C2 | semidirect |
| 5. #70687 | C2 | semidirect |
| 6. #67734 | C2 | semidirect |
| 7. #67664 | C2 | semidirect |
| 19. #5179 | C4 | semidirect |
| 20. #5147 | C4 | semidirect |
| 34. #1975 | D3 | semidirect |
| 356. C3 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83894 | 2 |
| C2×#4717 | 2 |
| C3×#1975 | 2 |
| #72080 | 2 |
| #70687 | 2 |
| #67734 | 2 |
| #67664 | 2 |
| #13024 | 3 |