Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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. #16810646 | C2 | semidirect |
| 4. C4×#11719919 | C2 | semidirect |
| 5. #16810384 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 9. Q8×Dic53 | C4 | semidirect |
| 10. Q8×Dic53 | C4 | semidirect |
| 13. D4×Dic53 | C4 | semidirect |
| 14. D4×Dic53 | C4 | semidirect |
| 72. Q8×C53 | C4⋊C4 | semidirect |
| 76. D4×C53 | C4⋊C4 | semidirect |
| 124. Dic53 | #104 | semidirect |
| 139. C53 | #1806 | semidirect |
| 204. Q8 | #11719919 | semidirect |
| 208. D4 | #11719919 | semidirect |