Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16811033 | C2 | semidirect |
| 3. #16811026 | C2 | semidirect |
| 5. #16810918 | C2 | semidirect |
| 6. #16810908 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 11. C53×#557 | C2 | semidirect |
| 63. #11719924 | Q8 | semidirect |
| 77. Q8×C53 | C2×Q8 | semidirect |
| 96. #88322 | C2×Q8 | semidirect |
| 117. #557 | D53 | semidirect |
| 128. C53 | #3386 | semidirect |
| 196. Q8 | Q8×D53 | semidirect |