Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. #16811645 | C2 | semidirect |
| 2. #16811559 | C2 | semidirect |
| 3. #16811474 | C2 | semidirect |
| 12. #13133217 | C4 | semidirect |
| 17. D4×Dic53 | C4 | semidirect |
| 19. #127×C53 | C4 | semidirect |
| 88. C53 | #1505 | semidirect |
| 91. #127 | #6157 | semidirect |