Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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. C22×Dic212 | C2 | semidirect |
| 3. #16811003 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 5. #16810834 | C2 | semidirect |
| 6. #16810781 | C2 | semidirect |
| 7. C4×Dic212 | C2 | semidirect |
| 54. Dic212 | D4 | direct (N × H) |
| 56. D4×C53 | Q16 | semidirect |
| 77. C22×C53 | C2×Q16 | semidirect |
| 81. C4×C53 | C2×Q16 | semidirect |
| 100. C53 | D4×Q16 | semidirect |
| 153. D4 | Dic212 | direct (N × H) |
| 169. C22 | C2×Dic212 | semidirect |
| 176. C4 | C2×Dic212 | semidirect |