Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #500×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #500 | D71 |
| hypocenter | C71 | #3353 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986723 | C2 | semidirect |
| 3. #17986336 | C2 | semidirect |
| 4. #17986326 | C2 | semidirect |
| 5. #17986281 | C2 | semidirect |
| 6. #17986276 | C2 | semidirect |
| 7. #17986246 | C2 | semidirect |
| 8. C4×#11765854 | C2 | semidirect |
| 9. #17986078 | C2 | semidirect |
| 10. #17986040 | C2 | semidirect |
| 11. #500×C71 | C2 | semidirect |
| 98. C8×C71 | #41 | semidirect |
| 123. C71 | #3353 | semidirect |
| 126. #500 | D71 | semidirect |
| 222. C8 | #11765866 | semidirect |