Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C2×C4⋊C8×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D53 |
| hypocenter | C53 | C2×#432 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810679 | C2 | direct (N × H) |
| 3. C2×C4⋊#88322 | C2 | semidirect |
| 5. C2×#13133127 | C2 | semidirect |
| 6. C2×C4⋊C8×C53 | C2 | semidirect |
| 16. C4⋊#88322 | C22 | semidirect |
| 18. #13133127 | C22 | semidirect |
| 21. C4⋊C8×C53 | C22 | semidirect |
| 90. C2×C53 | #432 | semidirect |
| 98. C2×C4⋊C8 | D53 | semidirect |
| 101. C53 | C2×#432 | semidirect |
| 114. C4⋊C8 | C2×D53 | semidirect |
| 185. C2 | #16810679 | direct (N × H) |