Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16811180 | C2 | semidirect |
| 3. #16810988 | C2 | semidirect |
| 4. #16810970 | C2 | semidirect |
| 5. #16810629 | C2 | semidirect |
| 6. C4×M16×C53 | C2 | semidirect |
| 9. #13133217 | C22 | semidirect |
| 13. #13133209 | C22 | semidirect |
| 17. #13133139 | C22 | semidirect |
| 20. #97×C53 | C22 | semidirect |
| 21. C4×C8×C53 | C22 | semidirect |
| 80. C4×M16 | D53 | semidirect |
| 81. C53 | #3138 | semidirect |
| 95. #97 | C2×D53 | semidirect |
| 96. C4×C8 | C2×D53 | semidirect |