Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13133151 | C2 | semidirect |
| 3. #16810425 | C2 | direct (N × H) |
| 4. C22×C16×C53 | C2 | semidirect |
| 8. C2×D424 | C4 | semidirect |
| 12. #13133151 | C22 | semidirect |
| 15. C2×C16×C53 | C22 | semidirect |
| 31. D424 | C2×C4 | semidirect |
| 63. C2×C53 | #357 | semidirect |
| 69. C22×C16 | D53 | semidirect |
| 72. C53 | C2×#357 | semidirect |
| 81. C2×C16 | C2×D53 | semidirect |
| 131. C2 | #16810425 | direct (N × H) |