Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
414 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 111 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×#2110 | C2 | semidirect |
| 3. #71448 | C2 | semidirect |
| 4. #71440 | C2 | semidirect |
| 5. #71427 | C2 | semidirect |
| 6. #69903 | C2 | semidirect |
| 7. #69897 | C2 | semidirect |
| 22. C2×#800 | C4 | semidirect |
| 23. C2×D48 | C4 | semidirect |
| 32. #2110 | D3 | semidirect |
| 328. C3 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4908 | 2 |
| C3×#2110 | 2 |
| #71448 | 2 |
| #71440 | 2 |
| #71427 | 2 |
| #69903 | 2 |
| #69897 | 2 |
| #13247 | 3 |