Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 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 | C22×D284 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #433×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #433 | D71 |
| hypocenter | C71 | #3123 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986611 | C2 | semidirect |
| 3. #17986341 | C2 | semidirect |
| 4. #17986300 | C2 | semidirect |
| 5. #17986205 | C2 | semidirect |
| 7. #17986101 | C2 | semidirect |
| 8. C4×#11765854 | C2 | semidirect |
| 9. #433×C71 | C2 | semidirect |
| 13. #14556128 | C22 | semidirect |
| 15. #14556120 | C22 | semidirect |
| 18. C4×Dic142 | C22 | semidirect |
| 24. #14556062 | C22 | semidirect |
| 25. #14556060 | C22 | semidirect |
| 26. #14556053 | C22 | semidirect |
| 27. #14556053 | C22 | semidirect |
| 31. C4⋊C8×C71 | C22 | semidirect |
| 33. #97×C71 | C22 | semidirect |
| 34. C4×C8×C71 | C22 | semidirect |
| 103. C71 | #3123 | semidirect |
| 112. #433 | D71 | semidirect |
| 130. C4⋊C8 | C2×D71 | semidirect |
| 136. #97 | C2×D71 | semidirect |
| 137. C4×C8 | C2×D71 | semidirect |