Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 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×#5068 | C2 | direct (N × H) |
| 4. C22×#810 | C2 | semidirect |
| 6. C22×C4×C3⋊C8 | C2 | semidirect |
| 11. C2×C3×#125 | C22 | semidirect |
| 19. #5068 | C22 | direct (N × H) |
| 20. C2×#810 | C22 | semidirect |
| 22. C2×C4×C3⋊C8 | C22 | semidirect |
| 23. C22×#125 | D3 | semidirect |
| 41. C3×#125 | C23 | semidirect |
| 52. #810 | C23 | semidirect |
| 54. C4×C3⋊C8 | C23 | semidirect |
| 59. C2×#125 | C2×D3 | semidirect |
| 113. #125 | C22×D3 | semidirect |
| 176. C22×C3 | #488 | semidirect |
| 210. C2×C3 | C2×#488 | semidirect |
| 217. C22 | #5068 | direct (N × H) |
| 226. C3 | C22×#488 | semidirect |
| 228. C2 | C2×#5068 | 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×#875 | 2 |
| C2×#5068 | 2 |
| C22×#810 | 2 |
| C22×#809 | 2 |
| C22×C4×C3⋊C8 | 2 |
| C22×#488 | 3 |