Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 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. #16811358 | C2 | semidirect |
| 2. D4×Dic106 | C2 | semidirect |
| 3. #16810984 | C2 | semidirect |
| 4. #16810970 | C2 | semidirect |
| 5. #16810912 | C2 | semidirect |
| 6. #16810908 | C2 | semidirect |
| 7. #16810840 | C2 | semidirect |
| 9. #16810753 | C2 | semidirect |
| 10. #16810732 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 135. C4×SD16 | D53 | semidirect |
| 136. C53 | #3373 | semidirect |