Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 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×#11719913 | C2 | semidirect |
| 3. C2×C4×Dic106 | C2 | semidirect |
| 4. #16810824 | C2 | direct (N × H) |
| 5. C2×#13133139 | C2 | semidirect |
| 6. C2×C4⋊C8×C53 | C2 | semidirect |
| 12. C2×#11719913 | C22 | semidirect |
| 16. C4×Dic106 | C22 | semidirect |
| 20. #13133139 | C22 | semidirect |
| 23. C4⋊C8×C53 | C22 | semidirect |
| 40. C2×Dic106 | D4 | semidirect |
| 57. C2×C4×C53 | SD16 | semidirect |
| 75. Dic106 | C2×D4 | semidirect |
| 87. C4×C53 | C2×SD16 | semidirect |
| 93. C2×C53 | #460 | semidirect |
| 102. C2×C4⋊C8 | D53 | semidirect |
| 104. C53 | C2×#460 | semidirect |
| 120. C4⋊C8 | C2×D53 | semidirect |
| 167. C2×C4 | #11719913 | semidirect |
| 187. C4 | C2×#11719913 | semidirect |
| 191. C2 | #16810824 | direct (N × H) |