Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#13133239 | C2 | semidirect |
| 2. C22×D424 | C2 | semidirect |
| 3. #16811061 | C2 | direct (N × H) |
| 4. C2×#13133162 | C2 | semidirect |
| 5. C2×D848 | C2 | semidirect |
| 6. C2×M32×C53 | C2 | semidirect |
| 10. #13133239 | C22 | semidirect |
| 11. C2×Dic212 | C22 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 17. C2×D424 | C22 | semidirect |
| 18. #13133162 | C22 | semidirect |
| 19. D848 | C22 | semidirect |
| 21. M32×C53 | C22 | semidirect |
| 22. C2×C16×C53 | C22 | semidirect |
| 40. Dic212 | C23 | semidirect |
| 45. D424 | C23 | semidirect |
| 47. C16×C53 | C23 | semidirect |
| 84. C2×C53 | #509 | semidirect |
| 93. C2×M32 | D53 | semidirect |
| 94. C53 | C2×#509 | semidirect |
| 109. M32 | C2×D53 | semidirect |
| 110. C2×C16 | C2×D53 | semidirect |
| 135. C16 | C22×D53 | semidirect |
| 173. C2 | #16811061 | direct (N × H) |