Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
836 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C22×#41×C53 | C2 |
| hypercenter | C22×#41 | D53 |
| hypocenter | C53 | #2432 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133215 | C2 | semidirect |
| 2. C2×#13133204 | C2 | semidirect |
| 3. C2×#13133196 | C2 | semidirect |
| 4. #16810537 | C2 | semidirect |
| 5. #16810530 | C2 | semidirect |
| 6. #16810526 | C2 | semidirect |
| 7. #16810496 | C2 | semidirect |
| 8. C4×C22⋊Dic53 | C2 | semidirect |
| 105. C2×Dic53 | #41 | semidirect |
| 146. C53 | #2432 | semidirect |