Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16811170 | C2 | semidirect |
| 2. #16811027 | C2 | semidirect |
| 3. #16810998 | C2 | semidirect |
| 4. #16810968 | C2 | semidirect |
| 5. #16810860 | C2 | semidirect |
| 6. #16810858 | C2 | semidirect |
| 7. #16810856 | C2 | semidirect |
| 8. C4×D424 | C2 | semidirect |
| 9. C4×#11719922 | C2 | semidirect |
| 10. C4×C8×D53 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 96. C4×D53 | D8 | semidirect |
| 99. C8×C53 | #41 | semidirect |
| 101. #88322 | #41 | semidirect |
| 137. C4×D8 | D53 | semidirect |
| 139. C53 | #3169 | semidirect |
| 229. C8 | #11719945 | semidirect |