Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
928 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 233 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×#380 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | #380 | D53 |
| hypocenter | C53 | #2339 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133179 | C2 | semidirect |
| 3. #16810528 | C2 | semidirect |
| 4. #16810499 | C2 | semidirect |
| 5. #16810485 | C2 | semidirect |
| 6. C4×C22⋊Dic53 | C2 | semidirect |
| 7. #95×D53 | C2 | semidirect |
| 8. C53×#380 | C2 | semidirect |
| 10. C2×#11719945 | C4 | semidirect |
| 31. C22×C4×C53 | C2×C4 | semidirect |
| 36. C2×C22⋊D53 | C2×C4 | semidirect |
| 47. C2×C4×D53 | C2×C4 | semidirect |
| 49. C2×Dic106 | C2×C4 | semidirect |
| 82. C2×Dic53 | #41 | semidirect |
| 83. D212 | C22⋊C4 | semidirect |
| 121. #380 | D53 | semidirect |
| 124. C53 | #2339 | semidirect |
| 162. C22×C4 | C4×D53 | semidirect |