Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 221 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. #16811106 | C2 | semidirect |
| 2. #16810724 | C2 | semidirect |
| 3. Q16×Dic53 | C2 | semidirect |
| 4. D8×Dic53 | C2 | semidirect |
| 5. C2×#13133151 | C2 | semidirect |
| 6. #16810624 | C2 | semidirect |
| 7. #16810578 | C2 | semidirect |
| 24. #135×C53 | C4 | semidirect |
| 30. #41×C53 | C2×C4 | semidirect |
| 38. Q16×C53 | C2×C4 | semidirect |
| 39. SD16×C53 | C2×C4 | semidirect |
| 40. D8×C53 | C2×C4 | semidirect |
| 41. C2×C8×C53 | C2×C4 | semidirect |
| 104. C53 | #2951 | semidirect |
| 106. #135 | Dic53 | semidirect |
| 126. #41 | C2×Dic53 | semidirect |
| 134. Q16 | C2×Dic53 | semidirect |
| 135. SD16 | C2×Dic53 | semidirect |
| 136. D8 | C2×Dic53 | semidirect |
| 139. C2×C8 | C2×Dic53 | semidirect |