Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #405×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #405 | D71 |
| hypocenter | C71 | #3136 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986627 | C2 | semidirect |
| 3. #17986364 | C2 | semidirect |
| 4. #17986359 | C2 | semidirect |
| 5. #17986354 | C2 | semidirect |
| 6. #17986346 | C2 | semidirect |
| 7. #17986005 | C2 | semidirect |
| 8. #17986001 | C2 | semidirect |
| 9. #17985996 | C2 | semidirect |
| 10. C2×#14556050 | C2 | semidirect |
| 11. #405×C71 | C2 | semidirect |
| 14. #14556128 | C22 | semidirect |
| 17. #14556120 | C22 | semidirect |
| 26. #14556053 | C22 | semidirect |
| 27. #14556053 | C22 | semidirect |
| 28. #14556053 | C22 | semidirect |
| 33. #14556050 | C22 | semidirect |
| 34. #14556050 | C22 | semidirect |
| 35. #14556050 | C22 | semidirect |
| 39. #97×C71 | C22 | semidirect |
| 40. C4×C8×C71 | C22 | semidirect |
| 136. C71 | #3136 | semidirect |
| 147. #405 | D71 | semidirect |
| 175. #97 | C2×D71 | semidirect |
| 176. C4×C8 | C2×D71 | semidirect |