Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 293 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 |
|---|---|---|
| 2. #16810665 | C2 | semidirect |
| 3. #16810661 | C2 | semidirect |
| 12. #13133151 | C22 | semidirect |
| 13. #13133149 | C22 | semidirect |
| 15. C2×M16×C53 | C4 | semidirect |
| 26. M16×C53 | C2×C4 | semidirect |
| 27. C2×C8×C53 | C2×C4 | semidirect |
| 71. C53 | #2911 | semidirect |
| 73. C2×M16 | Dic53 | semidirect |
| 93. M16 | C2×Dic53 | semidirect |
| 94. C2×C8 | C2×Dic53 | semidirect |