Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13133242 | C2 | semidirect |
| 2. C2×C4×D212 | C2 | semidirect |
| 3. #16810835 | C2 | semidirect |
| 4. #16810825 | C2 | semidirect |
| 5. #16810815 | C2 | semidirect |
| 6. #16810647 | C2 | semidirect |
| 7. #16810624 | C2 | semidirect |
| 8. C53×#532 | C2 | semidirect |
| 21. C4⋊#88322 | C22 | semidirect |
| 22. C4⋊#88322 | C22 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 24. #13133138 | C22 | semidirect |
| 26. C4⋊Q8×C53 | C22 | semidirect |
| 27. #127×C53 | C22 | semidirect |
| 28. #124×C53 | C22 | semidirect |
| 49. C2×D212 | D4 | semidirect |
| 119. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 131. #532 | D53 | semidirect |
| 138. C53 | #3036 | semidirect |
| 146. C4⋊Q8 | C2×D53 | semidirect |
| 147. #127 | C2×D53 | semidirect |
| 148. #124 | C2×D53 | semidirect |
| 250. C4 | #13133242 | semidirect |