Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 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. #16810663 | C2 | semidirect |
| 5. #16810384 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#428 | C2 | semidirect |
| 20. #13133133 | C4 | semidirect |
| 39. M16×C53 | C2×C4 | semidirect |
| 57. #11719917 | C2×C4 | semidirect |
| 117. #428 | D53 | semidirect |
| 122. C53 | #1856 | semidirect |
| 156. M16 | C4×D53 | semidirect |