Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16864030 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #472×C67 | C2 |
| socle | C2×C67 | D42 |
| hypercenter | #472 | D67 |
| hypocenter | C67 | #3290 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864213 | C2 | semidirect |
| 2. #16864206 | C2 | semidirect |
| 3. #16864197 | C2 | semidirect |
| 4. #16863779 | C2 | semidirect |
| 5. #16863672 | C2 | semidirect |
| 6. #16863658 | C2 | semidirect |
| 7. #16863576 | C2 | semidirect |
| 8. #16863567 | C2 | semidirect |
| 9. #16863512 | C2 | semidirect |
| 10. #16863511 | C2 | semidirect |
| 11. #472×C67 | C2 | semidirect |
| 12. #14524090 | C22 | semidirect |
| 16. #14524076 | C22 | semidirect |
| 27. C2×Dic268 | C22 | semidirect |
| 28. C2×#11761616 | C22 | semidirect |
| 31. #14524051 | C22 | semidirect |
| 33. #14524030 | C22 | semidirect |
| 34. #14523978 | C22 | semidirect |
| 35. #14523970 | C22 | semidirect |
| 37. #14523969 | C22 | semidirect |
| 38. #14523961 | C22 | semidirect |
| 39. C8×Dic67 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C67 | C22 | semidirect |
| 42. #131×C67 | C22 | semidirect |
| 43. #108×C67 | C22 | semidirect |
| 44. #100×C67 | C22 | semidirect |
| 150. C67 | #3290 | semidirect |
| 156. #472 | D67 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D67 | semidirect |
| 185. #131 | C2×D67 | semidirect |
| 188. #108 | C2×D67 | semidirect |
| 193. #100 | C2×D67 | semidirect |