Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
224 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C8 | C2×D53 |
| commutator | C2×C53 | C2×C4×C8 |
| Frattini | C42 | C22×D53 |
| Fitting | C2×C4×C8×C53 | C2 |
| socle | C22×C53 | C2×C42 |
| hypercenter | C2×C4×C8 | D53 |
| hypocenter | C53 | C8×M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4×C8 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16810345 | C2 | semidirect |
| 4. C8×#88322 | C2 | semidirect |
| 27. #11719917 | C8 | direct (N × H) |
| 41. C8×C53 | M16 | semidirect |
| 43. #88322 | C2×C8 | semidirect |
| 64. C53 | C8×M16 | semidirect |
| 102. C8 | #11719917 | direct (N × H) |