Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16810478 |
| commutator | C2×C4×C53 | C22×C4 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#421 | C2 |
| socle | C2×C53 | #379 |
| hypercenter | #421 | D53 |
| hypocenter | C53 | #1795 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810640 | C2 | semidirect |
| 3. #16810629 | C2 | semidirect |
| 4. #16810627 | C2 | semidirect |
| 5. #16810605 | C2 | semidirect |
| 6. #16810596 | C2 | semidirect |
| 7. C53×#421 | C2 | semidirect |
| 12. C2×#11719949 | C4 | semidirect |
| 18. C2×D4×D53 | C4 | semidirect |
| 19. C2×#11719917 | C22 | semidirect |
| 20. #13133176 | C22 | semidirect |
| 28. C2×M16×C53 | C22 | semidirect |
| 29. #117×C53 | C22 | semidirect |
| 156. #421 | D53 | semidirect |
| 161. C53 | #1795 | semidirect |
| 175. C2×M16 | C2×D53 | semidirect |
| 177. #117 | C2×D53 | semidirect |