Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 316 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. #16811593 | C2 | semidirect |
| 2. #16811468 | C2 | semidirect |
| 3. #16811466 | C2 | semidirect |
| 49. C23×C53 | M16 | semidirect |
| 54. C2×C4×C53 | M16 | semidirect |
| 102. C53 | #1465 | semidirect |
| 146. C23 | #11719940 | semidirect |
| 165. C2×C4 | #11719940 | semidirect |