Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 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. #79106 | C2 | semidirect |
| 3. #70658 | C2 | semidirect |
| 4. #70656 | C2 | semidirect |
| 5. C2×#4488 | C2 | semidirect |
| 6. C3×#1386 | C2 | semidirect |
| 7. #67814 | C2 | semidirect |
| 21. #4909 | C4 | semidirect |
| 23. #4908 | C4 | semidirect |
| 35. #1386 | D3 | semidirect |
| 45. C2×Dic12 | C2×C4 | semidirect |
| 55. C2×D24 | C2×C4 | semidirect |
| 64. C3×M32 | C2×C4 | semidirect |
| 190. M32 | C4×D3 | semidirect |
| 372. C3 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82009 | 2 |
| #79106 | 2 |
| #70658 | 2 |
| #70656 | 2 |
| C2×#4488 | 2 |
| C3×#1386 | 2 |
| #67814 | 2 |
| #13030 | 3 |