Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 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. C2×#13133157 | C2 | semidirect |
| 2. C2×#13133149 | C2 | semidirect |
| 3. #16810433 | C2 | direct (N × H) |
| 7. #13133157 | C22 | semidirect |
| 10. #13133149 | C22 | semidirect |
| 14. #135×C53 | C4 | semidirect |
| 16. C2×Q16×C53 | C4 | semidirect |
| 18. C2×D8×C53 | C4 | semidirect |
| 31. Q16×C53 | C2×C4 | semidirect |
| 35. D8×C53 | C2×C4 | semidirect |
| 84. C2×C53 | #360 | semidirect |
| 90. C53 | C2×#360 | semidirect |
| 94. #135 | Dic53 | semidirect |
| 96. C2×Q16 | Dic53 | semidirect |
| 98. C2×D8 | Dic53 | semidirect |
| 117. Q16 | C2×Dic53 | semidirect |
| 121. D8 | C2×Dic53 | semidirect |
| 169. C2 | #16810433 | direct (N × H) |