Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C4×#6157 | C2 | semidirect |
| 2. C2×#13133282 | C2 | semidirect |
| 3. #16811594 | C2 | semidirect |
| 4. #16811493 | C2 | semidirect |
| 17. #13133193 | C4 | semidirect |
| 18. #13133192 | C4 | semidirect |
| 19. #13133191 | C4 | semidirect |
| 24. C22⋊Q8×C53 | C4 | semidirect |
| 30. C2×Q8×C53 | C2×C4 | semidirect |
| 38. C2×D212 | C2×C4 | semidirect |
| 49. C4×#6157 | D4 | semidirect |
| 53. C4⋊C4×C53 | C2×C4 | semidirect |
| 59. C4⋊Dic53 | C2×C4 | semidirect |
| 99. C22×C53 | #104 | semidirect |
| 110. C2×D53 | #104 | semidirect |
| 135. C53 | #1896 | semidirect |
| 142. C22⋊Q8 | #6157 | semidirect |
| 158. C2×Q8 | C2×#6157 | semidirect |
| 182. C4⋊C4 | C2×#6157 | semidirect |
| 241. C22 | #13133282 | semidirect |