Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. C2×#13133285 | C2 | semidirect |
| 4. #16811574 | C2 | semidirect |
| 5. #16811496 | C2 | semidirect |
| 6. (C2×#6157)⋊C8 | C2 | semidirect |
| 23. #13133139 | C4 | semidirect |
| 24. #13133138 | C4 | semidirect |
| 25. #13133137 | C4 | semidirect |
| 26. #102×C53 | 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 | C4⋊C4 | semidirect |
| 93. D212 | C4⋊C4 | semidirect |
| 147. C53 | #1864 | semidirect |
| 165. #102 | #6157 | semidirect |
| 190. C2×C8 | C2×#6157 | semidirect |
| 198. C4⋊C4 | C2×#6157 | semidirect |
| 216. D4 | C4⋊#6157 | semidirect |