Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 225 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. #41×Dic53 | C2 | semidirect |
| 2. Q16×Dic53 | C2 | semidirect |
| 3. SD16×Dic53 | C2 | semidirect |
| 4. D8×Dic53 | C2 | semidirect |
| 5. #16810661 | C2 | semidirect |
| 6. #16810619 | C2 | semidirect |
| 7. C2×C8×Dic53 | 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 |
| 87. Dic53 | #135 | direct (N × H) |
| 101. C53 | C4×#135 | semidirect |
| 103. #135 | Dic53 | direct (N × H) |
| 123. #41 | C2×Dic53 | semidirect |
| 131. Q16 | C2×Dic53 | semidirect |
| 132. SD16 | C2×Dic53 | semidirect |
| 133. D8 | C2×Dic53 | semidirect |
| 136. C2×C8 | C2×Dic53 | semidirect |