Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C4×D212 | C2 | semidirect |
| 3. C2×#13133138 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. #16810385 | C2 | semidirect |
| 6. #16810378 | C2 | semidirect |
| 7. C53×#390 | C2 | semidirect |
| 12. C2×#11719922 | C4 | semidirect |
| 33. C2×D4×C53 | C2×C4 | semidirect |
| 63. C2×#88322 | C2×C4 | semidirect |
| 91. C2×C4×C53 | D8 | semidirect |
| 104. D212 | C22⋊C4 | semidirect |
| 151. #390 | D53 | semidirect |
| 154. C53 | #1879 | semidirect |
| 186. C2×D4 | C4×D53 | semidirect |
| 246. C2×C4 | #11719922 | semidirect |