Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#525 | C2 |
| hypercenter | #525 | D53 |
| hypocenter | C53 | #2978 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16810701 | C2 | semidirect |
| 2. #16810695 | C2 | semidirect |
| 3. #16810684 | C2 | semidirect |
| 4. #16810590 | C2 | semidirect |
| 5. #16810587 | C2 | semidirect |
| 8. C2×#11719917 | C22 | semidirect |
| 9. C22×#88322 | C22 | semidirect |
| 10. C4⋊#88322 | C22 | semidirect |
| 14. C22⋊#88322 | C22 | semidirect |
| 15. #13133128 | C22 | semidirect |
| 16. C4×#88322 | C22 | semidirect |
| 96. C53 | #2978 | semidirect |