Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #16810447 | C2 | semidirect |
| 5. #16810446 | C2 | semidirect |
| 6. #16810445 | C2 | semidirect |
| 7. C53×#365 | C2 | semidirect |
| 12. #13133156 | C4 | semidirect |
| 13. C16×D53 | C4 | semidirect |
| 36. C16×C53 | C2×C4 | semidirect |
| 37. #11719908 | C2×C4 | semidirect |
| 68. D53 | #365 | direct (N × H) |
| 75. #365 | D53 | direct (N × H) |
| 76. C53 | C2×#365 | semidirect |
| 106. C16 | C4×D53 | semidirect |