Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 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×Q8×D53 | C2 | semidirect |
| 2. C22×#11719913 | C2 | semidirect |
| 3. C22×#11719924 | C2 | semidirect |
| 5. #16810763 | C2 | direct (N × H) |
| 6. C2×#13133140 | C2 | semidirect |
| 7. C2×#13133129 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 14. C2×Q8×D53 | C22 | semidirect |
| 20. C2×#11719913 | C22 | semidirect |
| 22. C2×#11719924 | C22 | semidirect |
| 27. #13133140 | C22 | semidirect |
| 28. #13133129 | C22 | semidirect |
| 32. #103×C53 | C22 | semidirect |
| 37. C2×Q8×C53 | D4 | semidirect |
| 63. C2×Dic106 | D4 | semidirect |
| 81. C22×D53 | SD16 | semidirect |
| 85. Q8×C53 | C2×D4 | semidirect |
| 109. Dic106 | C2×D4 | semidirect |
| 123. C2×D53 | C2×SD16 | semidirect |
| 132. C2×C53 | #448 | semidirect |
| 144. C2×#103 | D53 | semidirect |
| 146. C53 | C2×#448 | semidirect |
| 169. #103 | C2×D53 | semidirect |
| 184. C2×Q8 | D212 | semidirect |
| 227. Q8 | C2×D212 | semidirect |
| 271. C2 | #16810763 | direct (N × H) |