Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C53 | C22×C42 |
| Fitting | C2×#95×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C2×#95 | D53 |
| hypocenter | C53 | #2275 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810474 | C2 | semidirect |
| 3. C4×C22⋊Dic53 | C2 | semidirect |
| 4. #16810470 | C2 | semidirect |
| 5. #16810468 | C2 | semidirect |
| 6. #95×D53 | C2 | semidirect |
| 7. C2×#95×C53 | C2 | semidirect |
| 10. C4×C22⋊D53 | C4 | semidirect |
| 24. C22×C4×C53 | C2×C4 | semidirect |
| 32. C2×C4×D53 | C2×C4 | semidirect |
| 33. C22⋊Dic53 | C2×C4 | semidirect |
| 34. #11719921 | C2×C4 | semidirect |
| 35. #11719919 | C2×C4 | semidirect |
| 37. C4×Dic53 | C2×C4 | semidirect |
| 50. C22⋊D53 | C42 | semidirect |
| 84. C2×#95 | D53 | semidirect |
| 85. C53 | #2275 | semidirect |
| 108. C22×C4 | C4×D53 | semidirect |