Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 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 | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #493×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #493 | D67 |
| hypocenter | C67 | #3155 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524067 | C2 | semidirect |
| 2. C2×#14524062 | C2 | semidirect |
| 3. C2×D8×D67 | C2 | semidirect |
| 4. #16863959 | C2 | semidirect |
| 5. #16863784 | C2 | semidirect |
| 6. #16863783 | C2 | semidirect |
| 7. #16863780 | C2 | semidirect |
| 8. #16863779 | C2 | semidirect |
| 9. #16863771 | C2 | semidirect |
| 10. #16863350 | C2 | semidirect |
| 11. #493×C67 | C2 | semidirect |
| 16. C2×Dic268 | C22 | semidirect |
| 17. C2×#11761617 | C22 | semidirect |
| 18. C2×#11761616 | C22 | semidirect |
| 19. C2×#11761616 | C22 | semidirect |
| 22. C2×#11761613 | C22 | semidirect |
| 26. #14524039 | C22 | semidirect |
| 27. #14524031 | C22 | semidirect |
| 28. #14524030 | C22 | semidirect |
| 32. #14523954 | C22 | semidirect |
| 33. #14523953 | C22 | semidirect |
| 34. C8×Dic67 | C22 | semidirect |
| 36. C2×D8×C67 | C22 | semidirect |
| 37. C2×D8×C67 | C22 | semidirect |
| 38. #127×C67 | C22 | semidirect |
| 39. C4×C8×C67 | C22 | semidirect |
| 59. #11761611 | D4 | semidirect |
| 62. C8×D67 | D4 | semidirect |
| 130. C67 | #3155 | semidirect |
| 140. #493 | D67 | semidirect |
| 155. C2×D8 | C2×D67 | semidirect |
| 156. C2×D8 | C2×D67 | semidirect |
| 160. #127 | C2×D67 | semidirect |
| 169. C4×C8 | C2×D67 | semidirect |