Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13133223 | C2 | semidirect |
| 2. #16811190 | C2 | semidirect |
| 3. #16810873 | C2 | semidirect |
| 4. #16810856 | C2 | semidirect |
| 5. #16810661 | C2 | semidirect |
| 6. #16810628 | C2 | semidirect |
| 7. C22×D8×C53 | C2 | semidirect |
| 11. C2×#11719912 | C22 | semidirect |
| 12. C2×C8×D53 | C22 | semidirect |
| 15. #13133188 | C22 | semidirect |
| 18. #13133151 | C22 | semidirect |
| 19. #13133149 | C22 | semidirect |
| 20. #13133138 | C22 | semidirect |
| 41. C2×C8×C53 | D4 | semidirect |
| 94. C22×D8 | D53 | semidirect |
| 101. C53 | #3058 | semidirect |
| 139. C2×C8 | C22⋊D53 | semidirect |