Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×D424 | C2 | semidirect |
| 2. #16811058 | C2 | direct (N × H) |
| 3. C2×#13133160 | C2 | semidirect |
| 4. C2×#13133158 | C2 | semidirect |
| 5. C2×#13133157 | C2 | semidirect |
| 6. C2×#135×C53 | C2 | semidirect |
| 11. C2×D424 | C22 | semidirect |
| 12. #13133160 | C22 | semidirect |
| 13. #13133158 | C22 | semidirect |
| 14. #13133157 | C22 | semidirect |
| 15. C2×#11719908 | C22 | semidirect |
| 18. #135×C53 | C22 | semidirect |
| 19. C2×Q16×C53 | C22 | semidirect |
| 21. C2×D8×C53 | C22 | semidirect |
| 36. Q16×C53 | C23 | semidirect |
| 39. D8×C53 | C23 | semidirect |
| 47. #11719908 | C23 | semidirect |
| 85. C2×C53 | #509 | semidirect |
| 88. C2×#135 | D53 | semidirect |
| 94. C53 | C2×#509 | semidirect |
| 98. #135 | C2×D53 | semidirect |
| 99. C2×Q16 | C2×D53 | semidirect |
| 105. C2×D8 | C2×D53 | semidirect |
| 124. Q16 | C22×D53 | semidirect |
| 130. D8 | C22×D53 | semidirect |
| 173. C2 | #16811058 | direct (N × H) |