Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
688 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #386×C67 | C2 |
| hypercenter | #386 | D67 |
| hypocenter | C67 | #2684 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524030 | C2 | semidirect |
| 3. #16863321 | C2 | semidirect |
| 4. #16863312 | C2 | semidirect |
| 5. #16863309 | C2 | semidirect |
| 6. #16863288 | C2 | semidirect |
| 7. #16863275 | C2 | semidirect |
| 8. #16863251 | C2 | semidirect |
| 9. #386×C67 | C2 | semidirect |
| 11. C22×Dic134 | C22 | semidirect |
| 15. C2×C4⋊Dic67 | C22 | semidirect |
| 18. C2×C22⋊Dic67 | C22 | semidirect |
| 24. C2×C4×Dic67 | C22 | semidirect |
| 25. C67⋊#95 | C22 | semidirect |
| 26. C67⋊#95 | C22 | semidirect |
| 27. C67⋊#95 | C22 | semidirect |
| 29. C23×C4×C67 | C22 | semidirect |
| 31. C2×C22⋊C4×C67 | C22 | semidirect |
| 32. #95×C67 | C22 | semidirect |
| 153. C67 | #2684 | semidirect |
| 161. #386 | D67 | semidirect |
| 167. C23×C4 | C2×D67 | semidirect |
| 180. C2×C22⋊C4 | C2×D67 | semidirect |
| 185. #95 | C2×D67 | semidirect |