Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C2×#127×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#127 | D71 |
| hypocenter | C71 | C2×#560 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986736 | C2 | direct (N × H) |
| 2. C2×#14556122 | C2 | semidirect |
| 3. C2×#14556109 | C2 | semidirect |
| 4. C2×#14556100 | C2 | semidirect |
| 5. C2×#14556096 | C2 | semidirect |
| 6. C2×#127×C71 | C2 | semidirect |
| 9. C23×Dic71 | C22 | semidirect |
| 10. #14556122 | C22 | semidirect |
| 11. #14556109 | C22 | semidirect |
| 12. #14556100 | C22 | semidirect |
| 13. #14556096 | C22 | semidirect |
| 14. C2×Dic71⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic71 | C22 | semidirect |
| 19. C22×D4×C71 | C22 | semidirect |
| 20. #127×C71 | C22 | semidirect |
| 21. C2×C42×C71 | C22 | semidirect |
| 29. C22×Dic71 | C23 | semidirect |
| 30. Dic71⋊C4 | C23 | semidirect |
| 32. C22⋊Dic71 | C23 | semidirect |
| 39. C2×D4×C71 | C23 | semidirect |
| 41. C42×C71 | C23 | semidirect |
| 74. C2×C71 | #560 | semidirect |
| 78. C71 | C2×#560 | semidirect |
| 80. C2×#127 | D71 | semidirect |
| 88. C22×D4 | C2×D71 | semidirect |
| 90. #127 | C2×D71 | semidirect |
| 99. C2×C42 | C2×D71 | semidirect |
| 110. C2×D4 | C22×D71 | semidirect |
| 119. C42 | C22×D71 | semidirect |
| 153. C2 | #17986736 | direct (N × H) |