Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1160 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C22×D4×C53 | C4 |
| hypercenter | C22×D4 | #6157 |
| hypocenter | C53 | #2308 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊#6157 | C2 | semidirect |
| 2. #16811571 | C2 | semidirect |
| 3. #16811566 | C2 | semidirect |
| 4. #16811564 | C2 | semidirect |
| 6. C23×#6157 | C22 | semidirect |
| 9. C2×C22⋊#6157 | C22 | semidirect |
| 10. C2×C22⋊#6157 | C22 | semidirect |
| 11. (C2×#6157)⋊C4 | C22 | semidirect |
| 14. C22×D212 | C4 | semidirect |
| 15. C22×C22⋊D53 | C4 | semidirect |
| 16. C22×C22⋊D53 | C4 | semidirect |
| 18. C2×D4×D53 | C4 | semidirect |
| 21. C22×D4×C53 | C4 | semidirect |
| 23. C24×C53 | C2×C4 | semidirect |
| 29. C23×D53 | C2×C4 | semidirect |
| 30. C23×D53 | C2×C4 | semidirect |
| 39. C2×D4×C53 | C2×C4 | semidirect |
| 40. C22×C4×C53 | C2×C4 | semidirect |
| 43. C2×C22⋊D53 | C2×C4 | semidirect |
| 44. C2×C22⋊D53 | C2×C4 | semidirect |
| 45. C22×Dic53 | C2×C4 | semidirect |
| 50. C2×D212 | C2×C4 | semidirect |
| 52. C2×C4×D53 | C2×C4 | semidirect |
| 60. C23×C53 | C22⋊C4 | semidirect |
| 76. C22×D53 | C22⋊C4 | semidirect |
| 77. C22×D53 | C22⋊C4 | semidirect |
| 141. C53 | #2308 | semidirect |
| 150. C22×D4 | #6157 | semidirect |
| 170. C24 | C2×#6157 | semidirect |
| 181. C2×D4 | C2×#6157 | semidirect |
| 189. C22×C4 | C2×#6157 | semidirect |
| 217. C23 | C22⋊#6157 | semidirect |