Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#13133144 | C2 | semidirect |
| 3. #16810628 | C2 | semidirect |
| 4. #16810526 | C2 | semidirect |
| 5. #16810391 | C2 | semidirect |
| 6. #16810384 | C2 | semidirect |
| 24. AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 40. C2×D4×C53 | C2×C4 | semidirect |
| 50. M16×C53 | C2×C4 | semidirect |
| 75. Q8×C53 | C22⋊C4 | semidirect |
| 83. D4×C53 | C22⋊C4 | semidirect |
| 140. C53 | #1883 | semidirect |
| 144. AGL(1,ℤ/8) | Dic53 | semidirect |
| 173. C2×D4 | C2×Dic53 | semidirect |
| 185. M16 | C2×Dic53 | semidirect |
| 208. Q8 | C22⋊Dic53 | semidirect |
| 216. D4 | C22⋊Dic53 | semidirect |