Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #3205 |
| 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. #17986547 | C2 | semidirect |
| 2. #127×D71 | C2 | semidirect |
| 3. #17986375 | C2 | semidirect |
| 4. #17986346 | C2 | semidirect |
| 5. #17986345 | C2 | semidirect |
| 6. #17986192 | C2 | semidirect |
| 7. #17986131 | C2 | semidirect |
| 8. #17986050 | C2 | semidirect |
| 9. #493×C71 | C2 | semidirect |
| 14. C2×#11765850 | C22 | semidirect |
| 15. #14556128 | C22 | semidirect |
| 24. D4×Dic71 | C22 | semidirect |
| 26. Dic71⋊C8 | C22 | semidirect |
| 27. #14556050 | C22 | semidirect |
| 28. #14556049 | C22 | semidirect |
| 30. C4×C71⋊C8 | C22 | semidirect |
| 31. C2×D8×C71 | C22 | semidirect |
| 33. #127×C71 | C22 | semidirect |
| 34. C4×C8×C71 | C22 | semidirect |
| 100. C4×D71 | D8 | semidirect |
| 133. C71 | #3205 | semidirect |
| 137. #493 | D71 | semidirect |
| 148. C2×D8 | C2×D71 | semidirect |
| 155. #127 | C2×D71 | semidirect |
| 167. C4×C8 | C2×D71 | semidirect |