Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16811235 | C2 | semidirect |
| 2. #16811018 | C2 | semidirect |
| 3. #16810995 | C2 | semidirect |
| 4. #16810987 | C2 | semidirect |
| 5. #16810977 | C2 | semidirect |
| 6. #16810842 | C2 | semidirect |
| 7. #16810820 | C2 | semidirect |
| 8. #16810785 | C2 | semidirect |
| 9. #16810774 | C2 | semidirect |
| 10. #16810684 | C2 | semidirect |
| 12. C2×#11719925 | C22 | semidirect |
| 15. C2×#11719923 | C22 | semidirect |
| 16. #13133217 | C22 | semidirect |
| 18. #13133209 | C22 | semidirect |
| 21. C4×Dic106 | C22 | semidirect |
| 22. C4⋊#88322 | C22 | semidirect |
| 23. #13133141 | C22 | semidirect |
| 26. #13133138 | C22 | semidirect |
| 28. #13133128 | C22 | semidirect |
| 29. C4×#88322 | C22 | semidirect |
| 134. C53 | #3222 | semidirect |