Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
392 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | #117×C53 | C4 |
| hypercenter | #117 | #6157 |
| hypocenter | C53 | #2921 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811648 | C2 | semidirect |
| 2. #16811647 | C2 | semidirect |
| 3. #16811628 | C2 | semidirect |
| 4. #16811627 | C2 | semidirect |
| 6. C4×#11719936 | C2 | semidirect |
| 10. #13133284 | C22 | semidirect |
| 11. C4⋊#88324 | C22 | semidirect |
| 14. #13133272 | C22 | semidirect |
| 15. C4×#88324 | C22 | semidirect |
| 112. C53 | #2921 | semidirect |