Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13133149 | C2 | semidirect |
| 3. C2×#13133142 | C2 | semidirect |
| 5. #16810529 | C2 | semidirect |
| 7. C2×C4×C8×C53 | C2 | semidirect |
| 12. C2×#11719913 | C4 | semidirect |
| 64. C2×C4×C53 | SD16 | semidirect |
| 87. C8×C53 | C22⋊C4 | semidirect |
| 117. C2×C4×C8 | D53 | semidirect |
| 120. C53 | #1968 | semidirect |
| 192. C2×C4 | #11719913 | semidirect |
| 200. C8 | #11719921 | semidirect |