Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #83173 | C2 | semidirect |
| 3. #71761 | C2 | semidirect |
| 4. C2×#4544 | C2 | semidirect |
| 5. #67655 | C2 | semidirect |
| 12. C3×#493 | C4 | semidirect |
| 39. C3×#127 | C2×C4 | semidirect |
| 51. C3×C4×C8 | C2×C4 | semidirect |
| 62. #493 | Dic3 | semidirect |
| 111. C4⋊Dic3 | D8 | semidirect |
| 131. #127 | C2×Dic3 | semidirect |
| 146. C4×C8 | C2×Dic3 | semidirect |
| 331. C3 | #9061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#493 | 2 |
| #83173 | 2 |
| #71761 | 2 |
| C2×#4544 | 2 |
| #67655 | 2 |
| #9061 | 3 |