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×#13133265 | C2 | semidirect |
| 2. C2×#13133248 | C2 | semidirect |
| 3. C2×#13133239 | C2 | semidirect |
| 4. #16811204 | C2 | semidirect |
| 5. #16810788 | C2 | semidirect |
| 6. #16810780 | C2 | semidirect |
| 7. #16810771 | C2 | semidirect |
| 8. #16810763 | C2 | semidirect |
| 9. #16810622 | C2 | semidirect |
| 10. #16810589 | C2 | semidirect |
| 11. C2×#103×C53 | C2 | semidirect |
| 47. C2×Q8×C53 | D4 | semidirect |
| 67. #11719945 | D4 | semidirect |
| 179. C2×#103 | D53 | semidirect |
| 181. C53 | #3013 | semidirect |
| 234. C2×Q8 | D212 | semidirect |