Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 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 | 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 | #3151 |
| 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×#14556152 | C2 | semidirect |
| 2. #17986547 | C2 | semidirect |
| 3. #127×D71 | C2 | semidirect |
| 4. #17986387 | C2 | semidirect |
| 5. #17986375 | C2 | semidirect |
| 6. #17986372 | C2 | semidirect |
| 7. #17986371 | C2 | semidirect |
| 8. C4×#11765848 | C2 | semidirect |
| 9. #493×C71 | C2 | semidirect |
| 14. C2×#11765854 | C22 | semidirect |
| 15. C2×#11765853 | C22 | semidirect |
| 16. C2×#11765850 | C22 | semidirect |
| 18. #14556128 | C22 | semidirect |
| 22. #14556115 | C22 | semidirect |
| 26. #14556038 | C22 | semidirect |
| 27. C4×C71⋊C8 | C22 | semidirect |
| 28. C2×D8×C71 | C22 | semidirect |
| 30. #127×C71 | C22 | semidirect |
| 31. C4×C8×C71 | C22 | semidirect |
| 48. #11765848 | D4 | semidirect |
| 85. C8×C71 | C2×D4 | semidirect |
| 86. C71⋊C8 | C2×D4 | semidirect |
| 97. C4×C71 | AGL(1,ℤ/8) | semidirect |
| 109. C71 | #3151 | semidirect |
| 115. #493 | D71 | semidirect |
| 126. C2×D8 | C2×D71 | semidirect |
| 133. #127 | C2×D71 | semidirect |
| 140. C4×C8 | C2×D71 | semidirect |
| 195. C8 | D4×D71 | semidirect |
| 209. C4 | #14556152 | semidirect |