Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 460 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 | #3325 |
| 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. #16864111 | C2 | semidirect |
| 2. #16864031 | C2 | semidirect |
| 3. #16863742 | C2 | semidirect |
| 4. #16863719 | C2 | semidirect |
| 5. #16863687 | C2 | semidirect |
| 6. #16863646 | C2 | semidirect |
| 7. #16863528 | C2 | semidirect |
| 8. C4×#11761613 | C2 | semidirect |
| 9. #16863473 | C2 | semidirect |
| 10. #16863399 | C2 | semidirect |
| 11. #459×C67 | C2 | semidirect |
| 15. C2×#11761611 | C22 | semidirect |
| 16. #14524043 | C22 | semidirect |
| 21. #14524014 | C22 | semidirect |
| 26. #14524001 | C22 | semidirect |
| 27. #14523976 | C22 | semidirect |
| 28. #14523975 | C22 | semidirect |
| 30. #14523964 | C22 | semidirect |
| 31. #14523964 | C22 | semidirect |
| 32. #14523964 | C22 | semidirect |
| 34. (C2×D67)⋊C8 | C22 | semidirect |
| 35. C4×C67⋊C8 | C22 | semidirect |
| 36. C2×D8×C67 | C22 | semidirect |
| 38. C4×D4×C67 | C22 | semidirect |
| 39. C4⋊C8×C67 | C22 | semidirect |
| 40. #102×C67 | C22 | semidirect |
| 141. C67 | #3325 | semidirect |
| 148. #459 | D67 | semidirect |
| 156. C2×D8 | C2×D67 | semidirect |
| 168. C4×D4 | C2×D67 | semidirect |
| 173. C4⋊C8 | C2×D67 | semidirect |
| 179. #102 | C2×D67 | semidirect |