Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C22×C67 | C23×C4 |
| Fitting | #386×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | #386 | D67 |
| hypocenter | C67 | #2372 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863300 | C2 | semidirect |
| 3. #16863290 | C2 | semidirect |
| 4. #16863284 | C2 | semidirect |
| 6. C22⋊C4×Dic67 | C2 | semidirect |
| 7. C4×C22⋊Dic67 | C2 | semidirect |
| 8. #16863241 | C2 | semidirect |
| 12. #14524030 | C4 | semidirect |
| 34. C2×Dic134 | C2×C4 | semidirect |
| 44. C22⋊Dic67 | C2×C4 | semidirect |
| 45. C22⋊Dic67 | C2×C4 | semidirect |
| 49. C4×Dic67 | C2×C4 | semidirect |
| 128. C67 | #2372 | semidirect |