Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #16811097 | C2 | semidirect |
| 3. #16810628 | C2 | semidirect |
| 4. C2×#13133133 | C2 | semidirect |
| 5. #16810384 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#418 | C2 | semidirect |
| 12. #13133213 | C4 | semidirect |
| 31. C2×D4×C53 | C2×C4 | semidirect |
| 46. C4⋊C4×C53 | D4 | semidirect |
| 51. C4⋊Dic53 | D4 | semidirect |
| 54. C4×Dic53 | C2×C4 | semidirect |
| 118. #418 | D53 | semidirect |
| 122. C53 | #1887 | semidirect |
| 154. C2×D4 | C4×D53 | semidirect |
| 165. C4⋊C4 | C22⋊D53 | semidirect |