Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
| 5. #16810863 | C2 | direct (N × H) |
| 6. C2×#13133150 | C2 | semidirect |
| 7. C2×#13133142 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 12. C2×#11719925 | C22 | semidirect |
| 25. #13133150 | C22 | semidirect |
| 26. #13133142 | C22 | semidirect |
| 30. #103×C53 | C22 | semidirect |
| 67. C22×D53 | Q16 | semidirect |
| 101. C2×D53 | C2×Q16 | semidirect |
| 111. C2×C53 | #467 | semidirect |
| 123. C2×#103 | D53 | semidirect |
| 124. C53 | C2×#467 | semidirect |
| 146. #103 | C2×D53 | semidirect |
| 227. C2 | #16810863 | direct (N × H) |