Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Frattini | C22 | C23×#6157 |
| Fitting | #117×C53 | C4 |
| hypercenter | #117 | #6157 |
| hypocenter | C53 | #2296 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16811574 | C2 | semidirect |
| 5. C4×C4⋊#6157 | C2 | semidirect |
| 18. #13133176 | C4 | semidirect |
| 19. #13133175 | C4 | semidirect |
| 20. #13133174 | C4 | semidirect |
| 21. #13133173 | C4 | semidirect |
| 25. #117×C53 | C4 | semidirect |
| 46. C4⋊C4×C53 | C2×C4 | semidirect |
| 48. C42×C53 | C2×C4 | semidirect |
| 51. C4⋊Dic53 | C2×C4 | semidirect |
| 52. #11719919 | C2×C4 | semidirect |
| 53. C4×Dic53 | C2×C4 | semidirect |
| 54. C4×Dic53 | C2×C4 | semidirect |
| 67. C2×C4×C53 | C4⋊C4 | semidirect |
| 71. C2×Dic53 | C4⋊C4 | semidirect |
| 76. C4×D53 | C4⋊C4 | semidirect |
| 77. C4×D53 | C4⋊C4 | semidirect |
| 113. C53 | #2296 | semidirect |
| 121. #117 | #6157 | semidirect |
| 151. C4⋊C4 | C2×#6157 | semidirect |
| 161. C42 | C2×#6157 | semidirect |
| 185. C2×C4 | C4⋊#6157 | semidirect |