Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1104 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 269 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 | C2×#117×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C2×#117 | D53 |
| hypocenter | C53 | #2309 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133176 | C2 | semidirect |
| 3. #16810525 | C2 | semidirect |
| 4. #16810524 | C2 | semidirect |
| 5. #16810478 | C2 | semidirect |
| 6. C2×#117×C53 | C2 | semidirect |
| 10. C22×D212 | C4 | semidirect |
| 14. C2×C4⋊Dic53 | C22 | semidirect |
| 16. C2×#11719921 | C22 | semidirect |
| 17. C2×C4×Dic53 | C22 | semidirect |
| 20. C2×C4⋊C4×C53 | C22 | semidirect |
| 22. C2×C42×C53 | C22 | semidirect |
| 65. C2×C4×C53 | C22⋊C4 | semidirect |
| 102. C2×#117 | D53 | semidirect |
| 106. C53 | #2309 | semidirect |
| 117. C2×C4⋊C4 | C2×D53 | semidirect |
| 122. C2×C42 | C2×D53 | semidirect |
| 169. C2×C4 | #11719921 | semidirect |