Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1008 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 210 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×D53⋊M16 | C2 | semidirect |
| 2. C2×#13133296 | C2 | semidirect |
| 3. #16811615 | C2 | direct (N × H) |
| 4. C2×#13133279 | C2 | semidirect |
| 8. D53⋊M16 | C22 | semidirect |
| 10. C2×D53⋊C8 | C22 | semidirect |
| 12. #13133296 | C22 | semidirect |
| 13. C2×C4⋊#6157 | C22 | semidirect |
| 16. #13133279 | C22 | semidirect |
| 18. C22×D212 | C4 | semidirect |
| 24. C2×D4×D53 | C4 | semidirect |
| 25. C2×D4×D53 | C4 | semidirect |
| 29. C22×D4×C53 | C4 | semidirect |
| 42. C2×D4×C53 | C2×C4 | semidirect |
| 57. D4×D53 | C2×C4 | semidirect |
| 62. C2×D212 | C2×C4 | semidirect |
| 75. C4⋊#6157 | C23 | semidirect |
| 79. D53⋊C8 | C23 | semidirect |
| 158. C2×C53 | #418 | semidirect |
| 162. D53 | #418 | semidirect |
| 169. C53 | C2×#418 | semidirect |
| 181. C22×D4 | #6157 | semidirect |
| 223. C2×D4 | C2×#6157 | semidirect |
| 325. C2 | #16811615 | direct (N × H) |