Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 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 | #461×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #461 | D67 |
| hypocenter | C67 | #3036 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524070 | C2 | semidirect |
| 2. #16863947 | C2 | semidirect |
| 3. C4×D4×D67 | C2 | semidirect |
| 4. #16863614 | C2 | semidirect |
| 5. #16863613 | C2 | semidirect |
| 6. #16863598 | C2 | semidirect |
| 7. #16863592 | C2 | semidirect |
| 8. #16863591 | C2 | semidirect |
| 9. #16863418 | C2 | semidirect |
| 10. #16863396 | C2 | semidirect |
| 11. #461×C67 | C2 | semidirect |
| 20. #14524040 | C22 | semidirect |
| 21. #14524032 | C22 | semidirect |
| 34. C4⋊(C67⋊C8) | C22 | semidirect |
| 35. Dic67⋊C8 | C22 | semidirect |
| 36. #14523967 | C22 | semidirect |
| 37. #14523965 | C22 | semidirect |
| 38. #14523963 | C22 | semidirect |
| 40. C4⋊Q8×C67 | C22 | semidirect |
| 42. C4⋊C8×C67 | C22 | semidirect |
| 43. #103×C67 | C22 | semidirect |
| 54. D4×D67 | D4 | semidirect |
| 146. C4×C67 | AGL(1,ℤ/8) | semidirect |
| 161. C67 | #3036 | semidirect |
| 168. #461 | D67 | semidirect |
| 182. C4⋊Q8 | C2×D67 | semidirect |
| 200. C4⋊C8 | C2×D67 | semidirect |
| 202. #103 | C2×D67 | semidirect |
| 311. C4 | #14524070 | semidirect |