Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 146 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 | #124×C53 | C4 |
| hypercenter | #124 | #6157 |
| hypocenter | C53 | #2981 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811656 | C2 | semidirect |
| 2. #16811655 | C2 | semidirect |
| 3. #16811652 | C2 | semidirect |
| 4. #16811650 | C2 | semidirect |
| 5. #16811646 | C2 | semidirect |
| 6. #16811642 | C2 | semidirect |
| 7. #16811598 | C2 | semidirect |
| 8. #16811596 | C2 | semidirect |
| 134. C53 | #2981 | semidirect |