Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
588 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C43×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C43 | D53 |
| hypocenter | C53 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #13133217 | C4 | direct (N × H) |
| 36. C42×C53 | Q8 | semidirect |
| 70. C4×C53 | C4×Q8 | semidirect |
| 71. C4×C53 | C4⋊Q8 | semidirect |
| 87. C53 | C4×C4⋊Q8 | semidirect |
| 119. C42 | Dic106 | semidirect |
| 152. C4 | C4×Dic106 | semidirect |
| 153. C4 | #13133217 | direct (N × H) |