Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
280 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 105 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×C4 | C22×D67 |
| commutator, socle | C23×C67 | C22×C4 |
| Fitting | #336×C67 | C2 |
| hypercenter | #336 | D67 |
| hypocenter | C67 | #1985 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 35. C2×C67⋊C8 | Q8 | semidirect |
| 51. C2×C8×C67 | Q8 | semidirect |
| 109. C67 | #1985 | semidirect |
| 153. C2×C8 | Dic134 | semidirect |