Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
740 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C22×Dic212 | C2 | semidirect |
| 4. #16810781 | C2 | direct (N × H) |
| 5. C2×#13133142 | C2 | semidirect |
| 15. C2×Dic212 | C22 | semidirect |
| 21. #13133142 | C22 | semidirect |
| 56. C23×C53 | Q16 | semidirect |
| 85. C22×C53 | C2×Q16 | semidirect |
| 96. C2×C53 | #451 | semidirect |
| 106. C53 | C2×#451 | semidirect |
| 156. C23 | Dic212 | semidirect |
| 185. C22 | C2×Dic212 | semidirect |
| 195. C2 | #16810781 | direct (N × H) |