Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 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. #16810676 | C2 | semidirect |
| 2. #16810489 | C2 | semidirect |
| 3. #16810357 | C2 | semidirect |
| 12. C4⋊Q8×C53 | C4 | semidirect |
| 13. #127×C53 | C4 | semidirect |
| 18. C4×D4×C53 | C4 | semidirect |
| 93. C53 | #1517 | semidirect |
| 95. C4⋊Q8 | Dic53 | semidirect |
| 96. #127 | Dic53 | semidirect |
| 101. C4×D4 | Dic53 | semidirect |