Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D284 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #424×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #424 | D71 |
| hypocenter | C71 | #3081 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986627 | C2 | semidirect |
| 3. #17986300 | C2 | semidirect |
| 4. #17986300 | C2 | semidirect |
| 5. #17986290 | C2 | semidirect |
| 6. #17986280 | C2 | semidirect |
| 7. #17986041 | C2 | semidirect |
| 8. #17986037 | C2 | semidirect |
| 11. #424×C71 | C2 | semidirect |
| 13. #14556128 | C22 | semidirect |
| 15. #14556120 | C22 | semidirect |
| 26. #14556062 | C22 | semidirect |
| 27. #14556062 | C22 | semidirect |
| 28. #14556062 | C22 | semidirect |
| 29. #14556060 | C22 | semidirect |
| 30. #14556060 | C22 | semidirect |
| 31. #14556060 | C22 | semidirect |
| 39. C4⋊C8×C71 | C22 | semidirect |
| 40. C4⋊C8×C71 | C22 | semidirect |
| 45. C2×D284 | Q8 | semidirect |
| 125. C71 | #3081 | semidirect |
| 134. #424 | D71 | semidirect |
| 160. C4⋊C8 | C2×D71 | semidirect |
| 161. C4⋊C8 | C2×D71 | semidirect |