Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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. #16811690 | C2 | semidirect |
| 2. #16811621 | C2 | semidirect |
| 3. #16811615 | C2 | semidirect |
| 4. #16811603 | C2 | semidirect |
| 5. #16811505 | C2 | semidirect |
| 6. #16811491 | C2 | semidirect |
| 22. C2×#11719913 | C4 | semidirect |
| 23. C2×#11719923 | C4 | semidirect |
| 24. C2×#11719922 | C4 | semidirect |
| 26. C2×D8×C53 | C4 | semidirect |
| 30. C2×D4×C53 | C2×C4 | semidirect |
| 44. C2×Dic106 | C2×C4 | semidirect |
| 59. C2×C8×C53 | C2×C4 | semidirect |
| 62. C2×#88322 | C2×C4 | semidirect |
| 136. C53 | #1904 | semidirect |
| 144. C2×D8 | #6157 | semidirect |
| 170. C2×D4 | C2×#6157 | semidirect |
| 184. C2×C8 | C2×#6157 | semidirect |