Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | D212 |
| commutator | C4×C53 | C22×C8 |
| Frattini | C42 | C22×D53 |
| Fitting | C82×C53 | C2 |
| socle | C22×C53 | C4×D4 |
| hypercenter | C82 | D53 |
| hypocenter | C53 | C8×SD16 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C8×Dic106 | C2 | semidirect |
| 4. #16810374 | C2 | semidirect |
| 5. #16810355 | C2 | semidirect |
| 7. C82×C53 | C2 | semidirect |
| 39. #11719913 | C8 | direct (N × H) |
| 53. Dic106 | C2×C8 | semidirect |
| 57. C8×C53 | C2×C8 | semidirect |
| 58. C8×C53 | SD16 | semidirect |
| 84. C82 | D53 | semidirect |
| 85. C53 | C8×SD16 | semidirect |
| 137. C8 | C8×D53 | semidirect |
| 138. C8 | #11719913 | direct (N × H) |