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 |
|---|---|---|
| 1. C22×C3×#125 | C2 | semidirect |
| 3. C2×#5067 | C2 | direct (N × H) |
| 4. C22×#809 | C2 | semidirect |
| 5. C22×#803 | C2 | semidirect |
| 10. C2×C3×#125 | C22 | semidirect |
| 17. #5067 | C22 | direct (N × H) |
| 18. C2×#809 | C22 | semidirect |
| 19. C2×#803 | C22 | semidirect |
| 21. C22×#125 | D3 | semidirect |
| 35. C3×#125 | C23 | semidirect |
| 45. #809 | C23 | semidirect |
| 46. #803 | C23 | semidirect |
| 53. C2×#125 | C2×D3 | semidirect |
| 98. #125 | C22×D3 | semidirect |
| 149. C22×C3 | #490 | semidirect |
| 179. C2×C3 | C2×#490 | semidirect |
| 186. C22 | #5067 | direct (N × H) |
| 194. C3 | C22×#490 | semidirect |
| 196. C2 | C2×#5067 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#125 | 2 |
| C22×#874 | 2 |
| C2×#5067 | 2 |
| C22×#809 | 2 |
| C22×#803 | 2 |
| C22×#490 | 3 |