Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #493×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #493 | D71 |
| hypocenter | C71 | D4×D8 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D8×D71 | C2 | semidirect |
| 2. #17986634 | C2 | semidirect |
| 3. #17986232 | C2 | semidirect |
| 4. #17986191 | C2 | semidirect |
| 5. #17986131 | C2 | semidirect |
| 6. C4×D568 | C2 | semidirect |
| 7. C8×D284 | C2 | semidirect |
| 8. #493×C71 | C2 | semidirect |
| 10. C2×D4×D71 | C22 | semidirect |
| 12. C2×#11765850 | C22 | semidirect |
| 14. C2×C8×D71 | C22 | semidirect |
| 16. #14556099 | C22 | semidirect |
| 19. C4×D284 | C22 | semidirect |
| 20. #14556062 | C22 | semidirect |
| 21. C4⋊(C71⋊C8) | C22 | semidirect |
| 22. #14556050 | C22 | semidirect |
| 23. #14556049 | C22 | semidirect |
| 24. (C2×D71)⋊C8 | C22 | semidirect |
| 25. C2×D8×C71 | C22 | semidirect |
| 26. C2×D8×C71 | C22 | semidirect |
| 27. #127×C71 | C22 | semidirect |
| 28. C4×C8×C71 | C22 | semidirect |
| 39. D568 | D4 | semidirect |
| 74. D284 | D8 | semidirect |
| 75. D284 | C2×D4 | semidirect |
| 80. C8×C71 | C2×D4 | semidirect |
| 92. C2×D71 | C2×D8 | semidirect |
| 94. C4×C71 | C2×D8 | semidirect |
| 106. C71 | D4×D8 | semidirect |
| 109. #493 | D71 | semidirect |
| 120. C2×D8 | C2×D71 | semidirect |
| 121. C2×D8 | C2×D71 | semidirect |
| 123. #127 | C2×D71 | semidirect |
| 134. C4×C8 | C2×D71 | semidirect |
| 187. C8 | D4×D71 | semidirect |
| 202. C4 | D8×D71 | semidirect |