Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 3. C2×#13133142 | C2 | semidirect |
| 5. #16810529 | C2 | semidirect |
| 6. #16810386 | C2 | semidirect |
| 7. C53×#336 | C2 | semidirect |
| 13. C2×#11719913 | C4 | semidirect |
| 47. C2×Dic106 | C2×C4 | semidirect |
| 53. C2×C8×C53 | C2×C4 | semidirect |
| 75. C2×C4×C53 | SD16 | semidirect |
| 140. #336 | D53 | semidirect |
| 141. C53 | #1877 | semidirect |
| 188. C2×C8 | C4×D53 | semidirect |
| 227. C2×C4 | #11719913 | semidirect |