Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16811330 | C2 | semidirect |
| 2. D4×Dic106 | C2 | semidirect |
| 3. #16811031 | C2 | semidirect |
| 4. #16811021 | C2 | semidirect |
| 5. #16810925 | C2 | semidirect |
| 6. #16810913 | C2 | semidirect |
| 7. #16810911 | C2 | semidirect |
| 8. #16810903 | C2 | semidirect |
| 9. #16810753 | C2 | semidirect |
| 52. D8×C53 | Q8 | semidirect |
| 78. D4×C53 | C2×Q8 | semidirect |
| 97. C8×C53 | C2×Q8 | semidirect |
| 133. C53 | #3384 | semidirect |
| 174. D8 | Dic106 | semidirect |
| 204. D4 | C2×Dic106 | semidirect |
| 220. C8 | C2×Dic106 | semidirect |