Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #16810450 | C2 | semidirect |
| 4. #16810427 | C2 | semidirect |
| 6. C4×#11719908 | C2 | semidirect |
| 7. C4×Q16×C53 | C2 | semidirect |
| 10. #13133160 | C4 | direct (N × H) |
| 24. Q16×C53 | C2×C4 | semidirect |
| 36. #11719908 | C2×C4 | semidirect |
| 59. C4×C53 | SD32 | semidirect |
| 69. C4×Q16 | D53 | semidirect |
| 75. C53 | C4×SD32 | semidirect |
| 92. Q16 | C4×D53 | semidirect |
| 128. C4 | #13133160 | direct (N × H) |