Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#13133149 | C2 | semidirect |
| 3. #16810434 | C2 | direct (N × H) |
| 4. C2×M32×C53 | C2 | semidirect |
| 8. #13133239 | C4 | semidirect |
| 10. C2×Dic212 | C4 | semidirect |
| 12. C2×D424 | C4 | semidirect |
| 15. #13133149 | C22 | semidirect |
| 18. M32×C53 | C22 | semidirect |
| 39. Dic212 | C2×C4 | semidirect |
| 41. D424 | C2×C4 | semidirect |
| 83. C2×C53 | #360 | semidirect |
| 87. C2×M32 | D53 | semidirect |
| 90. C53 | C2×#360 | semidirect |
| 102. M32 | C2×D53 | semidirect |
| 169. C2 | #16810434 | direct (N × H) |