Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13133216 | C2 | semidirect |
| 3. #16810911 | C2 | direct (N × H) |
| 4. C2×#13133149 | C2 | semidirect |
| 5. C2×#13133148 | C2 | semidirect |
| 6. C2×#13133146 | C2 | semidirect |
| 13. #13133216 | C22 | semidirect |
| 21. #13133149 | C22 | semidirect |
| 22. #13133148 | C22 | semidirect |
| 23. #13133146 | C22 | semidirect |
| 32. C2×D4×C53 | Q8 | semidirect |
| 65. D4×C53 | C2×Q8 | semidirect |
| 102. C2×C53 | #476 | semidirect |
| 114. C53 | C2×#476 | semidirect |
| 140. C2×D4 | Dic106 | semidirect |
| 172. D4 | C2×Dic106 | semidirect |
| 207. C2 | #16810911 | direct (N × H) |