Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #459×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #459 | D67 |
| hypocenter | C67 | #3217 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #127×D67 | C2 | semidirect |
| 2. #16863928 | C2 | semidirect |
| 3. #16863784 | C2 | semidirect |
| 4. #16863759 | C2 | semidirect |
| 5. #16863597 | C2 | semidirect |
| 6. #16863593 | C2 | semidirect |
| 7. #16863591 | C2 | semidirect |
| 8. #16863548 | C2 | semidirect |
| 9. #16863528 | C2 | semidirect |
| 10. #16863452 | C2 | semidirect |
| 11. #459×C67 | C2 | semidirect |
| 15. C2×#11761617 | C22 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 17. C2×#11761613 | C22 | semidirect |
| 23. #14524034 | C22 | semidirect |
| 24. #14524030 | C22 | semidirect |
| 28. C4×Dic134 | C22 | semidirect |
| 32. C4⋊(C67⋊C8) | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523964 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 38. C2×D8×C67 | C22 | semidirect |
| 40. C4×D4×C67 | C22 | semidirect |
| 41. C4⋊C8×C67 | C22 | semidirect |
| 42. #102×C67 | C22 | semidirect |
| 157. C67 | #3217 | semidirect |
| 165. #459 | D67 | semidirect |
| 175. C2×D8 | C2×D67 | semidirect |
| 189. C4×D4 | C2×D67 | semidirect |
| 193. C4⋊C8 | C2×D67 | semidirect |
| 197. #102 | C2×D67 | semidirect |