Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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. #16811622 | C2 | direct (N × H) |
| 4. C2×#13133282 | C2 | semidirect |
| 6. C2×#11719936 | C22 | semidirect |
| 8. D53⋊M16 | C22 | semidirect |
| 12. #13133296 | C22 | semidirect |
| 15. C2×C4×#6157 | C22 | semidirect |
| 16. #13133282 | C22 | semidirect |
| 21. C2×#11719949 | C4 | semidirect |
| 22. C2×#11719949 | C4 | semidirect |
| 26. C22×D212 | C4 | semidirect |
| 29. C22×Q8×C53 | C4 | semidirect |
| 36. C2×Q8×C53 | C2×C4 | semidirect |
| 48. #11719949 | C2×C4 | semidirect |
| 57. C2×D212 | C2×C4 | semidirect |
| 75. C4×#6157 | C23 | semidirect |
| 77. #11719936 | C23 | semidirect |
| 146. C2×C53 | #421 | semidirect |
| 157. C53 | C2×#421 | semidirect |
| 166. C22×Q8 | #6157 | semidirect |
| 197. C2×Q8 | C2×#6157 | semidirect |
| 301. C2 | #16811622 | direct (N × H) |