Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
376 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#13133149 | C2 | semidirect |
| 2. C2×#13133138 | C2 | semidirect |
| 3. C2×#13133127 | C2 | semidirect |
| 4. #16810526 | C2 | semidirect |
| 16. C2×D8×C53 | C4 | semidirect |
| 60. C8×C53 | C22⋊C4 | semidirect |
| 88. C53 | #1972 | semidirect |
| 92. C2×D8 | Dic53 | semidirect |
| 144. C8 | C22⋊Dic53 | semidirect |