Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #16811548 | C2 | semidirect |
| 4. #16811547 | C2 | semidirect |
| 14. #13133157 | C4 | semidirect |
| 16. C16×D53 | C4 | semidirect |
| 17. M32×C53 | C4 | semidirect |
| 32. C16×C53 | C2×C4 | semidirect |
| 33. #11719908 | C2×C4 | semidirect |
| 62. D53 | #365 | semidirect |
| 68. C53 | C2×#365 | semidirect |
| 74. M32 | #6157 | semidirect |
| 96. C16 | C2×#6157 | semidirect |