Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11719917 | C2 | semidirect |
| 3. C2×#13133145 | C2 | semidirect |
| 4. #16810383 | C2 | semidirect |
| 5. C4×C22⋊C4×C53 | C2 | semidirect |
| 12. #13133196 | C4 | semidirect |
| 13. #13133196 | C4 | semidirect |
| 14. #13133191 | C4 | semidirect |
| 15. #13133191 | C4 | semidirect |
| 58. #11719917 | D4 | semidirect |
| 103. C22×C53 | #104 | semidirect |
| 129. C4×C22⋊C4 | D53 | semidirect |
| 131. C53 | #1871 | semidirect |
| 232. C22 | #13133145 | semidirect |