Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 88 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×#13133285 | C2 | semidirect |
| 4. #16811497 | C2 | semidirect |
| 17. C22⋊#88322 | C4 | semidirect |
| 18. #13133129 | C4 | semidirect |
| 19. C22⋊C8×C53 | C4 | semidirect |
| 41. C2×C8×C53 | C2×C4 | semidirect |
| 42. C2×#88322 | C2×C4 | semidirect |
| 80. C22×C53 | #106 | semidirect |
| 88. C2×D53 | #106 | semidirect |
| 117. C53 | #1853 | semidirect |
| 130. C22⋊C8 | #6157 | semidirect |
| 150. C2×C8 | C2×#6157 | semidirect |
| 205. C22 | #13133285 | semidirect |