Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C16×D53 | C2 | semidirect |
| 3. #107×D53 | C2 | semidirect |
| 4. #16810425 | C2 | semidirect |
| 5. #16810424 | C2 | semidirect |
| 6. #16810423 | C2 | semidirect |
| 7. C53×#357 | C2 | semidirect |
| 12. D8×D53 | C4 | semidirect |
| 15. C2×#11719908 | C22 | semidirect |
| 17. #13133151 | C22 | semidirect |
| 20. C2×C16×C53 | C22 | semidirect |
| 21. #107×C53 | C22 | semidirect |
| 31. D8×C53 | C2×C4 | semidirect |
| 39. D424 | C2×C4 | semidirect |
| 87. D53 | #357 | direct (N × H) |
| 94. #357 | D53 | direct (N × H) |
| 95. C53 | C2×#357 | semidirect |
| 106. C2×C16 | C2×D53 | semidirect |
| 109. #107 | C2×D53 | semidirect |
| 122. D8 | C4×D53 | semidirect |