Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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. #16810666 | C2 | semidirect |
| 4. #16810492 | C2 | semidirect |
| 5. #16810392 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 15. #13133144 | C4 | semidirect |
| 52. C4×Dic53 | C2×C4 | semidirect |
| 56. #11719917 | C2×C4 | semidirect |
| 62. Q8×C53 | C4⋊C4 | semidirect |
| 66. D4×C53 | C4⋊C4 | semidirect |
| 120. C53 | #1859 | semidirect |
| 175. Q8 | #11719919 | semidirect |
| 179. D4 | #11719919 | semidirect |