Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator | C22×C53 | C23×C4 |
| Fitting | C53×#381 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | #381 | D53 |
| hypocenter | C53 | #2333 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810523 | C2 | semidirect |
| 3. #16810512 | C2 | semidirect |
| 4. #16810508 | C2 | semidirect |
| 5. #16810501 | C2 | semidirect |
| 6. #16810499 | C2 | semidirect |
| 7. C4×C22⋊Dic53 | C2 | semidirect |
| 8. #16810470 | C2 | semidirect |
| 9. C53×#381 | C2 | semidirect |
| 13. #13133191 | C4 | semidirect |
| 36. C22×C4×C53 | C2×C4 | semidirect |
| 43. C2×C22⋊D53 | C2×C4 | semidirect |
| 59. #11719921 | C2×C4 | semidirect |
| 60. C4⋊Dic53 | C2×C4 | semidirect |
| 141. #381 | D53 | semidirect |
| 144. C53 | #2333 | semidirect |
| 183. C22×C4 | C4×D53 | semidirect |