Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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×#386 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | #386 | D53 |
| hypocenter | C53 | #2374 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16810511 | C2 | semidirect |
| 4. #16810511 | C2 | semidirect |
| 5. #16810510 | C2 | semidirect |
| 6. #16810474 | C2 | semidirect |
| 7. C22⋊C4×Dic53 | C2 | semidirect |
| 8. C4×C22⋊Dic53 | C2 | semidirect |
| 11. #13133198 | C4 | semidirect |
| 44. C22×Dic53 | C2×C4 | semidirect |
| 54. C22⋊Dic53 | C2×C4 | semidirect |
| 57. #11719919 | C2×C4 | semidirect |
| 136. C53 | #2374 | semidirect |