Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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×C22⋊D71 |
| commutator | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #518×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #518 | D71 |
| hypocenter | C71 | #2949 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #518 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986476 | C2 | semidirect |
| 3. #17986099 | C2 | semidirect |
| 4. C4×#11765853 | C2 | semidirect |
| 5. #17986035 | C2 | semidirect |
| 6. #17986007 | C2 | semidirect |
| 8. #17985955 | C2 | semidirect |
| 11. C2×#11765853 | C4 | semidirect |
| 16. C4×Dic142 | C22 | semidirect |
| 20. #14556061 | C22 | semidirect |
| 21. #14556059 | C22 | semidirect |
| 22. #14556051 | C22 | semidirect |
| 24. #14556039 | C22 | semidirect |
| 25. C4×C71⋊C8 | C22 | semidirect |
| 34. C2×Dic142 | C2×C4 | semidirect |
| 37. #11765853 | C2×C4 | semidirect |
| 38. #11765853 | C2×C4 | semidirect |
| 40. C2×C71⋊C8 | C2×C4 | semidirect |
| 104. C71 | #2949 | semidirect |