Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #423×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #423 | D67 |
| hypocenter | C67 | #3036 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524071 | C2 | semidirect |
| 2. #16863946 | C2 | semidirect |
| 3. C2×C4×D268 | C2 | semidirect |
| 4. #16863612 | C2 | semidirect |
| 5. #16863602 | C2 | semidirect |
| 6. #16863592 | C2 | semidirect |
| 7. #16863398 | C2 | semidirect |
| 8. #423×C67 | C2 | semidirect |
| 15. #14524043 | C22 | semidirect |
| 16. #14524040 | C22 | semidirect |
| 17. #14524031 | C22 | semidirect |
| 28. #14523968 | C22 | semidirect |
| 29. #14523965 | C22 | semidirect |
| 32. C4⋊C8×C67 | C22 | semidirect |
| 33. C4⋊C8×C67 | C22 | semidirect |
| 42. C2×D268 | D4 | semidirect |
| 118. C4×C67 | AGL(1,ℤ/8) | semidirect |
| 130. C67 | #3036 | semidirect |
| 137. #423 | D67 | semidirect |
| 160. C4⋊C8 | C2×D67 | semidirect |
| 161. C4⋊C8 | C2×D67 | semidirect |
| 250. C4 | #14524071 | semidirect |