Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×D4×Dic53 | C2 | semidirect |
| 3. C2×#13133179 | C2 | semidirect |
| 4. #16810732 | C2 | direct (N × H) |
| 5. C2×#13133148 | C2 | semidirect |
| 6. C2×#13133139 | C2 | semidirect |
| 7. C2×#13133127 | C2 | semidirect |
| 8. C2×#102×C53 | C2 | semidirect |
| 12. C2×#11719922 | C4 | semidirect |
| 16. D4×Dic53 | C22 | semidirect |
| 18. #13133179 | C22 | semidirect |
| 23. #13133148 | C22 | semidirect |
| 24. #13133139 | C22 | semidirect |
| 25. #13133127 | C22 | semidirect |
| 29. #102×C53 | C22 | semidirect |
| 34. C2×D4×C53 | C2×C4 | semidirect |
| 45. C2×D212 | C2×C4 | semidirect |
| 54. #11719922 | C2×C4 | semidirect |
| 60. C2×#88322 | C2×C4 | semidirect |
| 73. D4×C53 | C22×C4 | semidirect |
| 89. D212 | C22×C4 | semidirect |
| 92. #88322 | C22×C4 | semidirect |
| 114. C2×C53 | #442 | semidirect |
| 125. C2×#102 | D53 | semidirect |
| 127. C53 | C2×#442 | semidirect |
| 147. #102 | C2×D53 | semidirect |
| 157. C2×D4 | C4×D53 | semidirect |
| 195. D4 | C2×C4×D53 | semidirect |
| 233. C2 | #16810732 | direct (N × H) |