Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 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 | #497×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #497 | D71 |
| hypocenter | C71 | C2×#497 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #497 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q16×D71 | C2 | semidirect |
| 3. C4⋊Q8×D71 | C2 | semidirect |
| 5. #17986394 | C2 | semidirect |
| 6. #17986393 | C2 | semidirect |
| 7. #17986392 | C2 | semidirect |
| 8. #17986391 | C2 | semidirect |
| 9. #17986390 | C2 | semidirect |
| 10. #97×D71 | C2 | semidirect |
| 11. #497×C71 | C2 | semidirect |
| 15. C2×Dic284 | C22 | semidirect |
| 16. C2×#11765855 | C22 | semidirect |
| 17. C2×#11765855 | C22 | semidirect |
| 24. #14556128 | C22 | semidirect |
| 26. #14556126 | C22 | semidirect |
| 34. #14556039 | C22 | semidirect |
| 35. #14556038 | C22 | semidirect |
| 36. C2×Q16×C71 | C22 | semidirect |
| 38. C4⋊Q8×C71 | C22 | semidirect |
| 40. #97×C71 | C22 | semidirect |
| 130. D71 | #497 | direct (N × H) |
| 132. C71 | C2×#497 | semidirect |
| 142. #497 | D71 | direct (N × H) |
| 151. C2×Q16 | C2×D71 | semidirect |
| 161. C4⋊Q8 | C2×D71 | semidirect |
| 172. #97 | C2×D71 | semidirect |