Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×D53 | C2 | semidirect |
| 3. C2×#13133145 | C2 | semidirect |
| 4. C2×#13133143 | C2 | semidirect |
| 5. #16810586 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#339 | C2 | semidirect |
| 13. #13133197 | C4 | semidirect |
| 14. #13133192 | C4 | semidirect |
| 38. C2×D212 | C2×C4 | semidirect |
| 48. C2×Dic106 | C2×C4 | semidirect |
| 52. C4⋊C4×C53 | C2×C4 | semidirect |
| 56. C42×C53 | D4 | semidirect |
| 62. C4×Dic53 | D4 | semidirect |
| 113. C2×D53 | #104 | semidirect |
| 136. #339 | D53 | semidirect |
| 137. C53 | #1896 | semidirect |
| 186. C4⋊C4 | C4×D53 | semidirect |
| 195. C42 | D212 | semidirect |