Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
604 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C53×#392 | C2 |
| hypercenter | #392 | D53 |
| hypocenter | C53 | #2598 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×Dic53 | C2 | semidirect |
| 2. C2×#13133173 | C2 | semidirect |
| 3. #16810563 | C2 | semidirect |
| 4. #16810559 | C2 | semidirect |
| 5. #16810537 | C2 | semidirect |
| 6. #16810517 | C2 | semidirect |
| 7. #16810503 | C2 | semidirect |
| 8. #16810503 | C2 | semidirect |
| 9. #16810495 | C2 | semidirect |
| 10. #16810490 | C2 | semidirect |
| 71. C4×Dic53 | D4 | semidirect |
| 157. C53 | #2598 | semidirect |