Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
192 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 73 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. C8×D212 | C2 | semidirect |
| 3. #16810373 | C2 | semidirect |
| 4. D4⋊#88322 | C2 | semidirect |
| 5. #16810350 | C2 | semidirect |
| 6. #16810345 | C2 | semidirect |
| 7. C8×D4×C53 | C2 | semidirect |
| 34. #11719922 | C8 | semidirect |
| 45. D4×C53 | C2×C8 | semidirect |
| 54. D212 | C2×C8 | semidirect |
| 63. #88322 | C2×C8 | semidirect |
| 86. C8×D4 | D53 | semidirect |
| 91. C53 | #1580 | semidirect |
| 131. D4 | C8×D53 | semidirect |