Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 161 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×#431 | C2 |
| hypercenter | #431 | D53 |
| hypocenter | C53 | #2981 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810702 | C2 | semidirect |
| 3. #16810693 | C2 | semidirect |
| 4. C8×D212 | C2 | semidirect |
| 5. #16810680 | C2 | semidirect |
| 6. #16810588 | C2 | semidirect |
| 7. C53×#431 | C2 | semidirect |
| 98. #431 | D53 | semidirect |
| 100. C53 | #2981 | semidirect |