Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16811199 | C2 | semidirect |
| 2. #16811010 | C2 | semidirect |
| 3. #16810995 | C2 | semidirect |
| 4. #16810993 | C2 | semidirect |
| 5. #16810980 | C2 | semidirect |
| 6. #16810838 | C2 | semidirect |
| 7. #16810828 | C2 | semidirect |
| 8. #16810766 | C2 | semidirect |
| 9. #16810761 | C2 | semidirect |
| 10. #16810684 | C2 | semidirect |
| 11. C53×#540 | C2 | semidirect |
| 121. #540 | D53 | semidirect |
| 132. C53 | #3221 | semidirect |