Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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×#6157 | C2 | semidirect |
| 2. #16811620 | C2 | semidirect |
| 3. C2×#13133281 | C2 | semidirect |
| 4. #16811603 | C2 | semidirect |
| 5. #16811506 | C2 | semidirect |
| 6. #16811495 | C2 | semidirect |
| 24. #13133250 | C4 | semidirect |
| 25. #13133247 | C4 | semidirect |
| 27. #13133243 | C4 | semidirect |
| 32. AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 36. C2×D4×C53 | C2×C4 | semidirect |
| 53. C2×Dic106 | C2×C4 | semidirect |
| 71. M16×C53 | C2×C4 | semidirect |
| 76. #11719917 | C2×C4 | semidirect |
| 158. C53 | #1906 | semidirect |
| 166. AGL(1,ℤ/8) | #6157 | semidirect |
| 199. C2×D4 | C2×#6157 | semidirect |
| 217. M16 | C2×#6157 | semidirect |