Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
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×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #459×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #459 | D71 |
| hypocenter | C71 | #3036 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556152 | C2 | semidirect |
| 2. #17986547 | C2 | semidirect |
| 3. C4×D4×D71 | C2 | semidirect |
| 4. #17986213 | C2 | semidirect |
| 5. #17986212 | C2 | semidirect |
| 6. #17986205 | C2 | semidirect |
| 7. #17986204 | C2 | semidirect |
| 8. #17986191 | C2 | semidirect |
| 9. #17986021 | C2 | semidirect |
| 10. #17985997 | C2 | semidirect |
| 11. #459×C71 | C2 | semidirect |
| 20. #14556128 | C22 | semidirect |
| 21. #14556115 | C22 | semidirect |
| 34. C4⋊(C71⋊C8) | C22 | semidirect |
| 35. Dic71⋊C8 | C22 | semidirect |
| 36. #14556053 | C22 | semidirect |
| 37. #14556051 | C22 | semidirect |
| 38. #14556049 | C22 | semidirect |
| 40. #127×C71 | C22 | semidirect |
| 42. C4⋊C8×C71 | C22 | semidirect |
| 43. #102×C71 | C22 | semidirect |
| 52. D4×D71 | D4 | semidirect |
| 145. C4×C71 | AGL(1,ℤ/8) | semidirect |
| 161. C71 | #3036 | semidirect |
| 170. #459 | D71 | semidirect |
| 183. #127 | C2×D71 | semidirect |
| 200. C4⋊C8 | C2×D71 | semidirect |
| 204. #102 | C2×D71 | semidirect |
| 311. C4 | #14556152 | semidirect |