Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1104 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 210 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 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C22×D4×C53 | C4 |
| hypercenter | C22×D4 | #6157 |
| hypocenter | C53 | #2309 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133296 | C2 | semidirect |
| 2. #16811575 | C2 | semidirect |
| 3. #16811564 | C2 | semidirect |
| 6. C2×C4⋊#6157 | C22 | semidirect |
| 8. C2×C22⋊#6157 | C22 | semidirect |
| 9. C2×C4×#6157 | C22 | semidirect |
| 11. C22×D212 | C4 | semidirect |
| 12. C22×C22⋊D53 | C4 | semidirect |
| 14. C2×D4×D53 | C4 | semidirect |
| 17. C22×D4×C53 | C4 | semidirect |
| 63. C2×C4×C53 | C22⋊C4 | semidirect |
| 66. C2×Dic53 | C22⋊C4 | semidirect |
| 69. C4×D53 | C22⋊C4 | semidirect |
| 103. C53 | #2309 | semidirect |
| 110. C22×D4 | #6157 | semidirect |
| 169. C2×C4 | C22⋊#6157 | semidirect |