Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 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. #16811278 | C2 | semidirect |
| 2. #16811277 | C2 | semidirect |
| 3. #16810974 | C2 | semidirect |
| 4. #16810960 | C2 | semidirect |
| 5. #16810903 | C2 | semidirect |
| 6. #16810868 | C2 | semidirect |
| 7. #16810828 | C2 | semidirect |
| 8. #16810765 | C2 | semidirect |
| 9. #16810702 | C2 | semidirect |
| 10. #16810621 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 83. D4×C53 | #41 | semidirect |
| 141. C4×D8 | D53 | semidirect |
| 144. C53 | #3330 | semidirect |
| 222. D4 | #11719945 | semidirect |