Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 68 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. D53⋊#108 | C2 | semidirect |
| 2. #16811616 | C2 | semidirect |
| 4. D53⋊#101 | C2 | semidirect |
| 6. #16811586 | C2 | semidirect |
| 22. C2×#11719913 | C4 | semidirect |
| 23. C2×#11719923 | C4 | semidirect |
| 24. C2×#11719924 | C4 | semidirect |
| 30. C2×SD16×C53 | C4 | semidirect |
| 141. C53 | #1977 | semidirect |
| 151. C2×SD16 | #6157 | semidirect |