Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4×#11719917 | C2 | semidirect |
| 4. #16810391 | C2 | semidirect |
| 5. C4×M16×C53 | C2 | semidirect |
| 15. #13133133 | C4 | direct (N × H) |
| 35. M16×C53 | C2×C4 | semidirect |
| 46. #11719917 | C2×C4 | semidirect |
| 85. C4×C53 | #100 | semidirect |
| 99. C4×M16 | D53 | semidirect |
| 101. C53 | C4×#100 | semidirect |
| 133. M16 | C4×D53 | semidirect |
| 182. C4 | #13133133 | direct (N × H) |