Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. C2×C8×#6157 | C2 | semidirect |
| 4. C4⋊C4×#6157 | C2 | semidirect |
| 5. #16811497 | C2 | semidirect |
| 6. #16811496 | C2 | semidirect |
| 11. D4×#6157 | C4 | semidirect |
| 17. #13133279 | C4 | semidirect |
| 23. #13133139 | C4 | semidirect |
| 24. #13133138 | C4 | semidirect |
| 25. #13133137 | C4 | semidirect |
| 26. #102×C53 | C4 | semidirect |
| 49. C4⋊#6157 | C2×C4 | semidirect |
| 54. D53⋊C8 | C2×C4 | semidirect |
| 55. C2×C8×C53 | C2×C4 | semidirect |
| 56. C4⋊C4×C53 | C2×C4 | semidirect |
| 57. C4⋊Dic53 | C2×C4 | semidirect |
| 59. C2×#88322 | C2×C4 | semidirect |
| 85. D4×C53 | C42 | semidirect |
| 93. D212 | C42 | semidirect |
| 123. #6157 | #102 | direct (N × H) |
| 147. C53 | C4×#102 | semidirect |
| 164. #102 | #6157 | direct (N × H) |
| 190. C2×C8 | C2×#6157 | semidirect |
| 197. C4⋊C4 | C2×#6157 | semidirect |
| 216. D4 | C4×#6157 | semidirect |