Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#13133236 | C2 | semidirect |
| 2. #16811272 | C2 | semidirect |
| 3. #16811001 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 5. #16810861 | C2 | semidirect |
| 6. #16810826 | C2 | semidirect |
| 7. #16810785 | C2 | semidirect |
| 8. #16810782 | C2 | semidirect |
| 9. D8×Dic53 | C2 | semidirect |
| 10. C8×C22⋊D53 | C2 | semidirect |
| 11. C2×#135×C53 | C2 | semidirect |
| 58. D8×C53 | D4 | semidirect |
| 129. Dic53 | #135 | semidirect |
| 138. C2×#135 | D53 | semidirect |
| 148. C53 | #3283 | semidirect |
| 198. D8 | C22⋊D53 | semidirect |