Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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. C4×#11719945 | C2 | semidirect |
| 3. C4×Dic212 | C2 | semidirect |
| 4. C4×#11719913 | C2 | semidirect |
| 5. C4×D424 | C2 | semidirect |
| 6. #16810661 | C2 | semidirect |
| 7. #16810620 | C2 | semidirect |
| 8. C2×C4×C8×C53 | C2 | semidirect |
| 10. #13133239 | C4 | direct (N × H) |
| 33. #11719945 | C2×C4 | semidirect |
| 39. C2×C8×C53 | C2×C4 | semidirect |
| 52. Dic212 | C2×C4 | semidirect |
| 53. D424 | C2×C4 | semidirect |
| 54. #11719913 | C2×C4 | semidirect |
| 83. C4×C53 | #135 | semidirect |
| 100. C2×C4×C8 | D53 | semidirect |
| 101. C53 | C4×#135 | semidirect |
| 135. C2×C8 | C4×D53 | semidirect |
| 178. C4 | #13133239 | direct (N × H) |