Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#11719925 | C2 | semidirect |
| 4. #16810862 | C2 | direct (N × H) |
| 5. C2×#13133150 | C2 | semidirect |
| 6. C2×#13133141 | C2 | semidirect |
| 7. C2×#13133140 | C2 | semidirect |
| 11. C2×#11719925 | C22 | semidirect |
| 21. #13133150 | C22 | semidirect |
| 22. #13133141 | C22 | semidirect |
| 23. #13133140 | C22 | semidirect |
| 66. C23×C53 | Q16 | semidirect |
| 99. C22×C53 | C2×Q16 | semidirect |
| 112. C2×C53 | #467 | semidirect |
| 124. C53 | C2×#467 | semidirect |
| 182. C23 | #11719925 | semidirect |
| 215. C22 | C2×#11719925 | semidirect |
| 227. C2 | #16810862 | direct (N × H) |