Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. C2×#13133276 | C2 | semidirect |
| 2. #16811528 | C2 | direct (N × H) |
| 6. #13133276 | C22 | semidirect |
| 8. C22×D212 | C4 | semidirect |
| 11. #13133214 | C4 | semidirect |
| 13. C2×C42×C53 | C4 | semidirect |
| 28. C2×D212 | C2×C4 | semidirect |
| 34. C42×C53 | C2×C4 | semidirect |
| 81. C2×C53 | #353 | semidirect |
| 89. C53 | C2×#353 | semidirect |
| 97. C2×C42 | #6157 | semidirect |
| 120. C42 | C2×#6157 | semidirect |
| 169. C2 | #16811528 | direct (N × H) |