Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
848 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#13133138 | C2 | semidirect |
| 2. C2×C22⋊#88322 | C2 | semidirect |
| 3. #16810483 | C2 | semidirect |
| 5. C22×#88322 | C22 | semidirect |
| 6. C2×C4⋊Dic53 | C22 | semidirect |
| 15. C22×D4×C53 | C4 | semidirect |
| 62. D4×C53 | C22⋊C4 | semidirect |
| 84. C22×C53 | #102 | semidirect |
| 106. C53 | #1786 | semidirect |
| 111. C22×D4 | Dic53 | semidirect |
| 164. D4 | C22⋊Dic53 | semidirect |
| 186. C22 | #13133138 | semidirect |