Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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. #16811098 | C2 | semidirect |
| 2. #16810640 | C2 | semidirect |
| 3. #16810628 | C2 | semidirect |
| 4. #16810597 | C2 | semidirect |
| 5. #16810394 | C2 | semidirect |
| 6. #16810380 | C2 | semidirect |
| 22. C2×SD16×C53 | C4 | semidirect |
| 23. C2×D8×C53 | C4 | semidirect |
| 30. C2×Q8×C53 | C2×C4 | semidirect |
| 36. C2×D4×C53 | C2×C4 | semidirect |
| 46. C2×C8×C53 | C2×C4 | semidirect |
| 123. C53 | #1904 | semidirect |
| 128. C2×SD16 | Dic53 | semidirect |
| 129. C2×D8 | Dic53 | semidirect |
| 146. C2×Q8 | C2×Dic53 | semidirect |
| 152. C2×D4 | C2×Dic53 | semidirect |
| 165. C2×C8 | C2×Dic53 | semidirect |