Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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 | #476×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #476 | D67 |
| hypocenter | C67 | #3077 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #476 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863951 | C2 | semidirect |
| 3. #16863695 | C2 | semidirect |
| 4. #16863694 | C2 | semidirect |
| 5. #16863683 | C2 | semidirect |
| 6. #16863677 | C2 | semidirect |
| 7. #16863676 | C2 | semidirect |
| 8. #16863435 | C2 | semidirect |
| 9. #16863418 | C2 | semidirect |
| 11. #476×C67 | C2 | semidirect |
| 15. #14524043 | C22 | semidirect |
| 16. #14524034 | C22 | semidirect |
| 30. #14523977 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. C4⋊(C67⋊C8) | C22 | semidirect |
| 34. Dic67⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C67 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 41. C4⋊C8×C67 | C22 | semidirect |
| 48. D4×D67 | Q8 | semidirect |
| 145. C67 | #3077 | semidirect |
| 151. #476 | D67 | semidirect |
| 161. C4⋊Q8 | C2×D67 | semidirect |
| 180. #106 | C2×D67 | semidirect |
| 183. C4⋊C8 | C2×D67 | semidirect |