Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×D212 | C2 | semidirect |
| 2. C22×D424 | C2 | semidirect |
| 3. C2×#13133191 | C2 | semidirect |
| 4. #16810759 | C2 | direct (N × H) |
| 5. C2×#13133139 | C2 | semidirect |
| 6. C2×C22⋊C8×C53 | C2 | semidirect |
| 12. C22×D212 | C22 | semidirect |
| 13. C22×D212 | C22 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 18. #13133191 | C22 | semidirect |
| 19. C2×C4⋊Dic53 | C22 | semidirect |
| 21. #13133139 | C22 | semidirect |
| 23. C22×C8×C53 | C22 | semidirect |
| 24. C22⋊C8×C53 | C22 | semidirect |
| 48. C2×D212 | D4 | semidirect |
| 50. C2×D212 | C23 | semidirect |
| 52. C2×C8×C53 | C23 | semidirect |
| 55. C4⋊Dic53 | C23 | semidirect |
| 59. C23×C53 | D8 | semidirect |
| 89. D212 | C2×D4 | semidirect |
| 96. C22×C53 | C2×D8 | semidirect |
| 114. C2×C53 | #447 | semidirect |
| 125. C2×C22⋊C8 | D53 | semidirect |
| 126. C53 | C2×#447 | semidirect |
| 138. C22×C8 | C2×D53 | semidirect |
| 144. C22⋊C8 | C2×D53 | semidirect |
| 173. C2×C8 | C22×D53 | semidirect |
| 191. C23 | D424 | semidirect |
| 225. C22 | C2×D424 | semidirect |
| 235. C2 | #16810759 | direct (N × H) |