Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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 | #496×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #496 | D67 |
| hypocenter | C67 | #3213 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #496 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863944 | C2 | semidirect |
| 2. #124×D67 | C2 | semidirect |
| 3. #16863783 | C2 | semidirect |
| 4. #16863756 | C2 | semidirect |
| 5. #16863755 | C2 | semidirect |
| 6. #16863613 | C2 | semidirect |
| 7. #16863609 | C2 | semidirect |
| 8. #16863533 | C2 | semidirect |
| 9. #16863528 | C2 | semidirect |
| 10. #16863451 | C2 | semidirect |
| 11. #496×C67 | C2 | semidirect |
| 15. C2×#11761616 | C22 | semidirect |
| 17. #14524043 | C22 | semidirect |
| 27. D4×Dic67 | C22 | semidirect |
| 31. Dic67⋊C8 | C22 | semidirect |
| 32. #14523968 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 37. #14523954 | C22 | semidirect |
| 38. C2×SD16×C67 | C22 | semidirect |
| 40. #127×C67 | C22 | semidirect |
| 42. #97×C67 | C22 | semidirect |
| 151. C67 | #3213 | semidirect |
| 155. #496 | D67 | semidirect |
| 167. C2×SD16 | C2×D67 | semidirect |
| 171. #127 | C2×D67 | semidirect |
| 193. #97 | C2×D67 | semidirect |