Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133247 | C2 | semidirect |
| 2. C2×#13133242 | C2 | semidirect |
| 3. C2×#13133205 | C2 | semidirect |
| 4. #16811015 | C2 | semidirect |
| 5. #16811010 | C2 | semidirect |
| 6. #16811005 | C2 | semidirect |
| 7. C4×#11719917 | C2 | semidirect |
| 8. C53×#532 | C2 | semidirect |
| 13. C2×#11719925 | C22 | semidirect |
| 14. C2×#11719923 | C22 | semidirect |
| 22. #13133128 | C22 | semidirect |
| 23. C4×#88322 | C22 | semidirect |
| 25. C4⋊Q8×C53 | C22 | semidirect |
| 26. #127×C53 | C22 | semidirect |
| 27. #124×C53 | C22 | semidirect |
| 59. #11719917 | D4 | semidirect |
| 109. #532 | D53 | semidirect |
| 115. C53 | #3153 | semidirect |
| 126. C4⋊Q8 | C2×D53 | semidirect |
| 127. #127 | C2×D53 | semidirect |
| 131. #124 | C2×D53 | semidirect |