Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
302 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 68 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. #16811634 | C2 | semidirect |
| 4. #16811569 | C2 | semidirect |
| 5. #16811502 | C2 | semidirect |
| 6. #16811494 | C2 | semidirect |
| 25. #13133145 | C4 | semidirect |
| 26. #13133144 | C4 | semidirect |
| 27. #13133143 | C4 | semidirect |
| 28. #104×C53 | C4 | semidirect |
| 59. M16×C53 | C2×C4 | semidirect |
| 60. C42×C53 | C2×C4 | semidirect |
| 62. C4×Dic53 | C2×C4 | semidirect |
| 63. #11719917 | C2×C4 | semidirect |
| 75. Q8×C53 | C4⋊C4 | semidirect |
| 77. D4×C53 | C4⋊C4 | semidirect |
| 88. D212 | C4⋊C4 | semidirect |
| 99. Dic106 | C4⋊C4 | semidirect |
| 139. C53 | #1859 | semidirect |
| 158. #104 | #6157 | semidirect |
| 180. M16 | C2×#6157 | semidirect |
| 197. C42 | C2×#6157 | semidirect |
| 202. Q8 | C4⋊#6157 | semidirect |
| 209. D4 | C4⋊#6157 | semidirect |