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×#832 | C2 | semidirect |
| 4. C2×#5071 | C2 | direct (N × H) |
| 5. C22×#803 | C2 | semidirect |
| 16. C2×#870 | C22 | semidirect |
| 17. C2×#832 | C22 | semidirect |
| 18. #5071 | C22 | direct (N × H) |
| 19. C2×#803 | C22 | semidirect |
| 44. #870 | C23 | semidirect |
| 45. #832 | C23 | semidirect |
| 46. #803 | C23 | semidirect |
| 152. C22×C3 | #490 | semidirect |
| 180. C2×C3 | C2×#490 | semidirect |
| 186. C22 | #5071 | direct (N × H) |
| 194. C3 | C22×#490 | semidirect |
| 196. C2 | C2×#5071 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#127 | 2 |
| C22×#870 | 2 |
| C22×#832 | 2 |
| C2×#5071 | 2 |
| C22×#803 | 2 |
| C22×#490 | 3 |