Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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. C22×#870 | C2 | semidirect |
| 3. C22×C3×#97 | C2 | semidirect |
| 4. C22×#821 | C2 | semidirect |
| 5. C2×#4713 | C2 | direct (N × H) |
| 16. C2×#870 | C22 | semidirect |
| 17. C2×C3×#97 | C22 | semidirect |
| 18. C2×#821 | C22 | semidirect |
| 19. #4713 | C22 | direct (N × H) |
| 24. C22×#97 | D3 | semidirect |
| 44. #870 | C23 | semidirect |
| 45. C3×#97 | C23 | semidirect |
| 46. #821 | C23 | semidirect |
| 59. C2×#97 | C2×D3 | semidirect |
| 105. #97 | C22×D3 | semidirect |
| 149. C22×C3 | #490 | semidirect |
| 179. C2×C3 | C2×#490 | semidirect |
| 186. C22 | #4713 | direct (N × H) |
| 194. C3 | C22×#490 | semidirect |
| 196. C2 | C2×#4713 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#874 | 2 |
| C22×#870 | 2 |
| C22×C3×#97 | 2 |
| C22×#821 | 2 |
| C2×#4713 | 2 |
| C22×#490 | 3 |