Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
| 5. #16810521 | C2 | semidirect |
| 6. #16810386 | C2 | semidirect |
| 7. C53×#336 | C2 | semidirect |
| 19. #13133139 | C4 | semidirect |
| 45. C2×C8×C53 | C2×C4 | semidirect |
| 53. C4⋊Dic53 | C2×C4 | semidirect |
| 88. D212 | C4⋊C4 | semidirect |
| 130. #336 | D53 | semidirect |
| 131. C53 | #1862 | semidirect |
| 169. C2×C8 | C4×D53 | semidirect |