Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #3205 |
| 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. #16863944 | C2 | semidirect |
| 2. #127×D67 | C2 | semidirect |
| 3. #16863772 | C2 | semidirect |
| 4. #16863743 | C2 | semidirect |
| 5. #16863742 | C2 | semidirect |
| 6. #16863589 | C2 | semidirect |
| 7. #16863528 | C2 | semidirect |
| 8. #16863447 | C2 | semidirect |
| 9. #493×C67 | C2 | semidirect |
| 14. C2×#11761613 | C22 | semidirect |
| 15. #14524043 | C22 | semidirect |
| 24. D4×Dic67 | C22 | semidirect |
| 26. Dic67⋊C8 | C22 | semidirect |
| 27. #14523965 | C22 | semidirect |
| 28. #14523964 | C22 | semidirect |
| 30. C4×C67⋊C8 | C22 | semidirect |
| 31. C2×D8×C67 | C22 | semidirect |
| 33. #127×C67 | C22 | semidirect |
| 34. C4×C8×C67 | C22 | semidirect |
| 100. C4×D67 | D8 | semidirect |
| 133. C67 | #3205 | semidirect |
| 137. #493 | D67 | semidirect |
| 148. C2×D8 | C2×D67 | semidirect |
| 155. #127 | C2×D67 | semidirect |
| 167. C4×C8 | C2×D67 | semidirect |