Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #16810702 | C2 | semidirect |
| 3. C8×D212 | C2 | semidirect |
| 4. #16810374 | C2 | semidirect |
| 5. #16810352 | C2 | semidirect |
| 6. #16810352 | C2 | semidirect |
| 7. C53×#322 | C2 | semidirect |
| 52. D212 | M16 | semidirect |
| 90. #322 | D53 | semidirect |
| 91. C53 | #1586 | semidirect |