Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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. #79167 | C2 | semidirect |
| 3. #70658 | C2 | semidirect |
| 4. #70656 | C2 | semidirect |
| 5. #70652 | C2 | semidirect |
| 6. C3×#1384 | C2 | semidirect |
| 7. #67813 | C2 | semidirect |
| 22. C2×#800 | C4 | semidirect |
| 23. C2×D48 | C4 | semidirect |
| 33. #1384 | D3 | semidirect |
| 42. C2×Dic12 | C2×C4 | semidirect |
| 51. C2×D24 | C2×C4 | semidirect |
| 60. C2×C3×C16 | C2×C4 | semidirect |
| 172. C2×C16 | C4×D3 | semidirect |
| 340. C3 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4908 | 2 |
| #79167 | 2 |
| #70658 | 2 |
| #70656 | 2 |
| #70652 | 2 |
| C3×#1384 | 2 |
| #67813 | 2 |
| #13033 | 3 |