Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 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×#13133153 | C2 | semidirect |
| 3. #16810437 | C2 | direct (N × H) |
| 4. C2×M32×C53 | C2 | semidirect |
| 14. #13133153 | C22 | semidirect |
| 17. M32×C53 | C22 | semidirect |
| 76. C2×C53 | #361 | semidirect |
| 80. C2×M32 | D53 | semidirect |
| 83. C53 | C2×#361 | semidirect |
| 94. M32 | C2×D53 | semidirect |
| 155. C2 | #16810437 | direct (N × H) |