Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×#13133151 | C2 | semidirect |
| 3. C2×#13133150 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C53×#340 | C2 | semidirect |
| 19. #13133129 | C4 | semidirect |
| 42. C2×C8×C53 | C2×C4 | semidirect |
| 55. C2×#88322 | C2×C4 | semidirect |
| 105. C2×D53 | #107 | semidirect |
| 130. #340 | D53 | semidirect |
| 131. C53 | #1852 | semidirect |
| 169. C2×C8 | C4×D53 | semidirect |