Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
672 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | C22×C22⋊C4×C67 | C2 |
| hypercenter | C22×C22⋊C4 | D67 |
| hypocenter | C67 | #2561 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524022 | C2 | semidirect |
| 2. #16863321 | C2 | semidirect |
| 3. #16863308 | C2 | semidirect |
| 4. #16863290 | C2 | semidirect |
| 5. #16863259 | C2 | semidirect |
| 7. C4×C22⋊Dic67 | C2 | semidirect |
| 9. C22×Dic134 | C22 | semidirect |
| 11. C2×C4⋊Dic67 | C22 | semidirect |
| 12. C2×Dic67⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic67 | C22 | semidirect |
| 18. C67⋊#95 | C22 | semidirect |
| 19. C67⋊#95 | C22 | semidirect |
| 20. C67⋊#95 | C22 | semidirect |
| 111. C67 | #2561 | semidirect |