Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13133216 | C2 | semidirect |
| 3. #16810902 | C2 | direct (N × H) |
| 4. C2×#13133150 | C2 | semidirect |
| 5. C2×#13133146 | C2 | semidirect |
| 8. C2×#107×C53 | C2 | semidirect |
| 14. #13133216 | C22 | semidirect |
| 21. #13133150 | C22 | semidirect |
| 22. #13133146 | C22 | semidirect |
| 28. #107×C53 | C22 | semidirect |
| 38. C2×D212 | Q8 | semidirect |
| 79. D212 | C2×Q8 | semidirect |
| 101. C2×C53 | #474 | semidirect |
| 110. C2×#107 | D53 | semidirect |
| 114. C53 | C2×#474 | semidirect |
| 131. #107 | C2×D53 | semidirect |
| 207. C2 | #16810902 | direct (N × H) |