Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #16811104 | C2 | semidirect |
| 3. C2×#13133145 | C2 | semidirect |
| 4. #16810628 | C2 | semidirect |
| 5. #16810392 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 7. C53×#390 | C2 | semidirect |
| 10. #13133243 | C4 | semidirect |
| 34. C2×D4×C53 | C2×C4 | semidirect |
| 64. #11719917 | C2×C4 | semidirect |
| 95. D212 | C22⋊C4 | semidirect |
| 100. Dic106 | C22⋊C4 | semidirect |
| 137. #390 | D53 | semidirect |
| 140. C53 | #1883 | semidirect |
| 174. C2×D4 | C4×D53 | semidirect |