Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 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 | C22×C67 | C22×C8 |
| Fitting | #336×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | #336 | D67 |
| hypocenter | C67 | #1923 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Dic67⋊C8 | C2 | semidirect |
| 4. C2×C4×C67⋊C8 | C2 | semidirect |
| 6. #16863150 | C2 | semidirect |
| 7. #336×C67 | C2 | semidirect |
| 40. (C2×D67)⋊C4 | C8 | semidirect |
| 123. C67 | #1923 | semidirect |
| 130. #336 | D67 | semidirect |