Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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 | #459×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #459 | D71 |
| hypocenter | C71 | #3109 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986547 | C2 | semidirect |
| 2. C4×D4×D71 | C2 | semidirect |
| 3. #17986316 | C2 | semidirect |
| 4. #17986290 | C2 | semidirect |
| 5. #17986289 | C2 | semidirect |
| 6. #17986191 | C2 | semidirect |
| 7. #17986131 | C2 | semidirect |
| 8. #17986111 | C2 | semidirect |
| 9. #17986108 | C2 | semidirect |
| 10. #17986055 | C2 | semidirect |
| 11. #459×C71 | C2 | semidirect |
| 16. #14556128 | C22 | semidirect |
| 23. D4×Dic71 | C22 | semidirect |
| 30. #14556060 | C22 | semidirect |
| 31. #14556059 | C22 | semidirect |
| 32. C4⋊(C71⋊C8) | C22 | semidirect |
| 35. #14556049 | C22 | semidirect |
| 37. #14556038 | C22 | semidirect |
| 39. #127×C71 | C22 | semidirect |
| 41. C4⋊C8×C71 | C22 | semidirect |
| 42. #102×C71 | C22 | semidirect |
| 96. D4×C71 | #41 | semidirect |
| 112. D284 | #41 | semidirect |
| 155. C71 | #3109 | semidirect |
| 162. #459 | D71 | semidirect |
| 173. #127 | C2×D71 | semidirect |
| 191. C4⋊C8 | C2×D71 | semidirect |
| 195. #102 | C2×D71 | semidirect |
| 256. D4 | #11765864 | semidirect |