Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 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×C4 | C22×D53 |
| commutator | C22×C53 | C2×C42 |
| Fitting | C53×#336 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | #336 | D53 |
| hypocenter | C53 | #1729 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #16810378 | C2 | semidirect |
| 5. #16810377 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C53×#336 | C2 | semidirect |
| 11. C2×#11719912 | C4 | semidirect |
| 16. C2×C8×D53 | C4 | semidirect |
| 115. #336 | D53 | semidirect |
| 116. C53 | #1729 | semidirect |