Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 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 | C23×C53 | C24 |
| Frattini | C23 | C23×D53 |
| Fitting | C2×#95×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C2×#95 | D53 |
| hypocenter | C53 | C2×#393 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic106 | C2 | semidirect |
| 4. #16810536 | C2 | direct (N × H) |
| 5. C2×#13133124 | C2 | semidirect |
| 6. C2×#95×C53 | C2 | semidirect |
| 10. C22×Dic106 | C22 | semidirect |
| 17. #13133124 | C22 | semidirect |
| 20. #95×C53 | C22 | semidirect |
| 26. C23×D53 | Q8 | semidirect |
| 62. C22×D53 | C2×Q8 | semidirect |
| 99. C2×C53 | #393 | semidirect |
| 111. C2×#95 | D53 | semidirect |
| 112. C53 | C2×#393 | semidirect |
| 126. #95 | C2×D53 | semidirect |
| 205. C2 | #16810536 | direct (N × H) |