Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#13133242 | C2 | semidirect |
| 2. #16811187 | C2 | semidirect |
| 3. C2×#13133214 | C2 | semidirect |
| 4. #16810629 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 7. C2×#104×C53 | C2 | semidirect |
| 35. C2×Q8×C53 | D4 | semidirect |
| 37. C2×D4×C53 | D4 | semidirect |
| 55. C2×D212 | D4 | semidirect |
| 60. C42×C53 | D4 | semidirect |
| 65. C4⋊Dic53 | D4 | semidirect |
| 68. #11719917 | D4 | semidirect |
| 142. C2×#104 | D53 | semidirect |
| 146. C53 | #2002 | semidirect |
| 174. C2×Q8 | D212 | semidirect |
| 191. C2×D4 | D212 | semidirect |
| 208. C42 | C22⋊D53 | semidirect |