Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
3464 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C26×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C26 | D53 |
| hypocenter | C53 | C2×#379 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C26 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊Dic53 | C2 | semidirect |
| 2. #16810479 | C2 | direct (N × H) |
| 4. C23×Dic53 | C22 | semidirect |
| 6. C2×C22⋊Dic53 | C22 | semidirect |
| 8. C25×C53 | C4 | semidirect |
| 16. C24×C53 | C2×C4 | semidirect |
| 21. C22×Dic53 | C23 | semidirect |
| 29. C23×C53 | C22⋊C4 | semidirect |
| 42. C22×C53 | C2×C22⋊C4 | semidirect |
| 49. C2×C53 | #379 | semidirect |
| 55. C53 | C2×#379 | semidirect |
| 57. C25 | Dic53 | semidirect |
| 68. C24 | C2×Dic53 | semidirect |
| 81. C23 | C22⋊Dic53 | semidirect |
| 94. C22 | C2×C22⋊Dic53 | semidirect |
| 100. C2 | #16810479 | direct (N × H) |