Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
496 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 188 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 | C4⋊Q8×C53 | C4 |
| hypercenter | C4⋊Q8 | #6157 |
| hypocenter | C53 | #2369 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #13133217 | C4 | semidirect |
| 15. #13133216 | C4 | semidirect |
| 16. #13133215 | C4 | semidirect |
| 19. C4⋊Q8×C53 | C4 | semidirect |
| 32. C4⋊#6157 | Q8 | semidirect |
| 87. C53 | #2369 | semidirect |
| 92. C4⋊Q8 | #6157 | semidirect |