Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 1. C2×#13133245 | C2 | semidirect |
| 2. C2×#13133242 | C2 | semidirect |
| 3. #16811201 | C2 | semidirect |
| 4. C2×#13133145 | C2 | semidirect |
| 5. #16810525 | C2 | semidirect |
| 6. #16810391 | C2 | semidirect |
| 7. C2×#104×C53 | C2 | semidirect |
| 55. C2×D212 | D4 | semidirect |
| 59. M16×C53 | D4 | semidirect |
| 72. #11719917 | D4 | semidirect |
| 157. C2×#104 | D53 | semidirect |
| 160. C53 | #2006 | semidirect |
| 218. M16 | C22⋊D53 | semidirect |