Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 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. #16811634 | C2 | semidirect |
| 4. #16811567 | C2 | semidirect |
| 5. #16811502 | C2 | semidirect |
| 6. #16811494 | C2 | semidirect |
| 25. #13133145 | C4 | semidirect |
| 26. #13133144 | C4 | semidirect |
| 27. #13133143 | C4 | semidirect |
| 28. #104×C53 | C4 | semidirect |
| 58. M16×C53 | C2×C4 | semidirect |
| 59. C42×C53 | C2×C4 | semidirect |
| 61. C4×Dic53 | C2×C4 | semidirect |
| 62. #11719917 | C2×C4 | semidirect |
| 138. C53 | #1860 | semidirect |
| 156. #104 | #6157 | semidirect |
| 179. M16 | C2×#6157 | semidirect |
| 195. C42 | C2×#6157 | semidirect |