Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
136 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. #16811025 | C2 | semidirect |
| 3. #16810451 | C2 | semidirect |
| 4. #16810449 | C2 | semidirect |
| 7. C53×C4⋊C16 | C2 | semidirect |
| 67. C4⋊C16 | D53 | semidirect |
| 70. C53 | #2228 | semidirect |