Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 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 | #486×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #486 | D71 |
| hypocenter | C71 | C2×#486 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #486 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊Q8×D71 | C2 | semidirect |
| 3. #17986347 | C2 | semidirect |
| 4. #17986346 | C2 | semidirect |
| 5. #17986345 | C2 | semidirect |
| 6. #17986344 | C2 | semidirect |
| 7. #102×D71 | C2 | semidirect |
| 8. C4×C8×D71 | C2 | semidirect |
| 9. #486×C71 | C2 | semidirect |
| 15. #14556128 | C22 | semidirect |
| 17. #14556127 | C22 | semidirect |
| 26. #14556050 | C22 | semidirect |
| 27. #14556049 | C22 | semidirect |
| 28. #14556048 | C22 | semidirect |
| 29. C4×C71⋊C8 | C22 | semidirect |
| 30. C8×Dic71 | C22 | semidirect |
| 31. C4⋊Q8×C71 | C22 | semidirect |
| 33. #102×C71 | C22 | semidirect |
| 34. C4×C8×C71 | C22 | semidirect |
| 125. D71 | #486 | direct (N × H) |
| 127. C71 | C2×#486 | semidirect |
| 134. #486 | D71 | direct (N × H) |
| 146. C4⋊Q8 | C2×D71 | semidirect |
| 158. #102 | C2×D71 | semidirect |
| 161. C4×C8 | C2×D71 | semidirect |