Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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×#390 | C2 |
| hypercenter | #390 | D53 |
| hypocenter | C53 | #2432 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133217 | C2 | semidirect |
| 3. C2×#13133204 | C2 | semidirect |
| 4. C2×#13133197 | C2 | semidirect |
| 5. #16810539 | C2 | semidirect |
| 6. #16810528 | C2 | semidirect |
| 7. #16810498 | C2 | semidirect |
| 8. C4×#11719921 | C2 | semidirect |
| 9. C53×#390 | C2 | semidirect |
| 89. C2×C4×C53 | #41 | semidirect |
| 143. #390 | D53 | semidirect |
| 146. C53 | #2432 | semidirect |
| 243. C2×C4 | #11719947 | semidirect |