Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 7. D53⋊C16 | C4 | semidirect |
| 12. #13133153 | C4 | semidirect |
| 14. #108×C53 | C4 | semidirect |
| 62. C53 | #1383 | semidirect |
| 71. #108 | #6157 | semidirect |