Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
440 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 149 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×D424 | C2 | semidirect |
| 2. C2×#13133158 | C2 | direct (N × H) |
| 3. C22×#11719908 | C2 | semidirect |
| 4. C22×D8×C53 | C2 | semidirect |
| 7. C2×D424 | C22 | semidirect |
| 8. #13133158 | C22 | direct (N × H) |
| 9. C2×#11719908 | C22 | semidirect |
| 12. C2×D8×C53 | C22 | semidirect |
| 22. D8×C53 | C23 | semidirect |
| 26. D424 | C23 | semidirect |
| 27. #11719908 | C23 | semidirect |
| 43. C22×C53 | D16 | semidirect |
| 51. C2×C53 | C2×D16 | semidirect |
| 55. C22×D8 | D53 | semidirect |
| 58. C53 | C22×D16 | semidirect |
| 64. C2×D8 | C2×D53 | semidirect |
| 78. D8 | C22×D53 | semidirect |
| 99. C22 | #13133158 | direct (N × H) |
| 105. C2 | C2×#13133158 | direct (N × H) |