Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#13133264 | C2 | semidirect |
| 2. C2×#13133250 | C2 | semidirect |
| 3. C2×#13133237 | C2 | semidirect |
| 4. #16811204 | C2 | semidirect |
| 5. #16810786 | C2 | semidirect |
| 6. #16810780 | C2 | semidirect |
| 7. #16810769 | C2 | semidirect |
| 8. #16810763 | C2 | semidirect |
| 9. C2×#13133140 | C2 | semidirect |
| 10. #16810591 | C2 | semidirect |
| 11. C53×#417 | C2 | semidirect |
| 46. #41×C53 | D4 | semidirect |
| 79. C2×Dic106 | D4 | semidirect |
| 178. #417 | D53 | semidirect |
| 181. C53 | #3013 | semidirect |
| 224. #41 | D212 | semidirect |