Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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. #16810680 | C2 | semidirect |
| 3. #16810362 | C2 | semidirect |
| 4. C4×M16×C53 | C2 | semidirect |
| 15. #13133128 | C22 | semidirect |
| 18. #97×C53 | C22 | semidirect |
| 87. C4×M16 | D53 | semidirect |
| 89. C53 | #1527 | semidirect |
| 103. #97 | C2×D53 | semidirect |