Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#11719923 | C2 | semidirect |
| 2. C2×#13133197 | C2 | semidirect |
| 4. C2×#13133142 | C2 | semidirect |
| 5. C2×#13133129 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C2×#102×C53 | C2 | semidirect |
| 56. C2×Dic106 | D4 | semidirect |
| 61. C4⋊C4×C53 | D4 | semidirect |
| 70. C2×#88322 | D4 | semidirect |
| 85. C22×D53 | SD16 | semidirect |
| 162. C2×#102 | D53 | semidirect |
| 165. C53 | #2000 | semidirect |
| 226. C4⋊C4 | C22⋊D53 | semidirect |