Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C22×C42×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C22×C42 | D53 |
| hypocenter | C53 | #2296 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16810521 | C2 | semidirect |
| 5. C4×#11719919 | C2 | semidirect |
| 8. #13133176 | C4 | semidirect |
| 38. C4⋊Dic53 | C2×C4 | semidirect |
| 41. C4×Dic53 | C2×C4 | semidirect |
| 50. C2×C4×C53 | C4⋊C4 | semidirect |
| 87. C53 | #2296 | semidirect |
| 135. C2×C4 | #11719919 | semidirect |