Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
620 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 620 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. #83174 | C2 | semidirect |
| 3. #71813 | C2 | semidirect |
| 4. #71760 | C2 | semidirect |
| 5. #67666 | C2 | semidirect |
| 11. C3×#493 | C4 | semidirect |
| 12. C3×#492 | C4 | semidirect |
| 34. C3×C4⋊Q8 | C2×C4 | semidirect |
| 37. C3×#127 | C2×C4 | semidirect |
| 46. C3×C4×C8 | C2×C4 | semidirect |
| 57. #493 | Dic3 | semidirect |
| 58. #492 | Dic3 | semidirect |
| 108. C4⋊Q8 | C2×Dic3 | semidirect |
| 111. #127 | C2×Dic3 | semidirect |
| 123. C4×C8 | C2×Dic3 | semidirect |
| 255. C3 | #9428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3151 | 2 |
| #83174 | 2 |
| #71813 | 2 |
| #71760 | 2 |
| #67666 | 2 |
| #9428 | 3 |