Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
196 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×#6157 |
| commutator | C2×C53 | C2×C4×C8 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C4×C8×C53 | C4 |
| socle | C22×C53 | C22×C8 |
| hypercenter | C4×C8 | #6157 |
| hypocenter | C53 | C4×M32 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16811512 | C2 | semidirect |
| 3. C4×#11719910 | C2 | semidirect |
| 5. #13133292 | C4 | direct (N × H) |
| 25. #11719910 | C2×C4 | semidirect |
| 41. C4×C53 | M32 | semidirect |
| 54. C53 | C4×M32 | semidirect |
| 93. C4 | #13133292 | direct (N × H) |