Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #16811091 | C2 | semidirect |
| 3. #16810717 | C2 | semidirect |
| 4. #16810710 | C2 | semidirect |
| 5. #16810705 | C2 | semidirect |
| 6. #16810617 | C2 | semidirect |
| 7. C2×C8×Dic53 | C2 | semidirect |
| 8. C53×#427 | C2 | semidirect |
| 10. #13133239 | C4 | semidirect |
| 33. #11719945 | C2×C4 | semidirect |
| 38. C2×C8×C53 | C2×C4 | semidirect |
| 52. Dic212 | C2×C4 | semidirect |
| 53. D424 | C2×C4 | semidirect |
| 54. #11719913 | C2×C4 | semidirect |
| 87. Dic53 | #135 | semidirect |
| 98. #427 | D53 | semidirect |
| 101. C53 | C4×#135 | semidirect |
| 136. C2×C8 | C4×D53 | semidirect |