Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 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×#13133240 | C2 | semidirect |
| 2. #16811292 | C2 | semidirect |
| 3. #16810998 | C2 | semidirect |
| 4. #16810859 | C2 | semidirect |
| 5. #16810856 | C2 | semidirect |
| 6. #16810821 | C2 | semidirect |
| 7. #16810768 | C2 | semidirect |
| 8. #16810767 | C2 | semidirect |
| 9. Q16×Dic53 | C2 | semidirect |
| 10. C8×C22⋊D53 | C2 | semidirect |
| 11. C2×#135×C53 | C2 | semidirect |
| 59. Q16×C53 | D4 | semidirect |
| 134. Dic53 | #135 | semidirect |
| 144. C2×#135 | D53 | semidirect |
| 154. C53 | #3287 | semidirect |
| 202. Q16 | C22⋊D53 | semidirect |