Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1564 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | C23×D4×C71 | C2 |
| hypercenter | C23×D4 | D71 |
| hypocenter | C71 | #2403 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D71 | C2 | semidirect |
| 2. C2×#14556097 | C2 | semidirect |
| 3. C2×#14556096 | C2 | semidirect |
| 4. #17985907 | C2 | semidirect |
| 5. #17985879 | C2 | semidirect |
| 6. #17985878 | C2 | semidirect |
| 7. #17985855 | C2 | semidirect |
| 8. C23×D4×C71 | C2 | semidirect |
| 9. C24×D71 | C22 | semidirect |
| 13. C22×C22⋊D71 | C22 | semidirect |
| 14. C22×C22⋊D71 | C22 | semidirect |
| 15. C23×Dic71 | C22 | semidirect |
| 18. C2×C22⋊Dic71 | C22 | semidirect |
| 19. C2×C22⋊Dic71 | C22 | semidirect |
| 20. C2×C22⋊Dic71 | C22 | semidirect |
| 21. C2×C22⋊Dic71 | C22 | semidirect |
| 22. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 23. C71⋊#95 | C22 | semidirect |
| 25. C25×C71 | C22 | semidirect |
| 29. C22×D4×C71 | C22 | semidirect |
| 30. C23×C4×C71 | C22 | semidirect |
| 45. C2×C22⋊D71 | D4 | semidirect |
| 62. C24×C71 | D4 | semidirect |
| 73. C2×D4×C71 | D4 | semidirect |
| 101. C23×C71 | C2×D4 | semidirect |
| 111. C22×D71 | C2×D4 | semidirect |
| 117. C2×C4×C71 | C2×D4 | semidirect |
| 127. C2×Dic71 | C2×D4 | semidirect |
| 145. C22×C71 | #120 | semidirect |
| 146. C22×C71 | #120 | semidirect |
| 170. C71 | #2403 | semidirect |
| 172. C23×D4 | D71 | semidirect |
| 181. C25 | C2×D71 | semidirect |
| 190. C22×D4 | C2×D71 | semidirect |
| 192. C23×C4 | C2×D71 | semidirect |
| 213. C24 | C22⋊D71 | semidirect |
| 234. C2×D4 | C22⋊D71 | semidirect |
| 280. C23 | C2×C22⋊D71 | semidirect |
| 297. C2×C4 | C2×C22⋊D71 | semidirect |
| 321. C22 | #14556096 | semidirect |
| 322. C22 | #14556097 | semidirect |