Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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 | #3041 |
| 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. C2×#14556156 | C2 | semidirect |
| 2. C22×D568 | C2 | semidirect |
| 3. #17986568 | C2 | semidirect |
| 4. #17986473 | C2 | semidirect |
| 5. #17986215 | C2 | semidirect |
| 6. #17986195 | C2 | semidirect |
| 7. #17986005 | C2 | semidirect |
| 8. #17985996 | C2 | semidirect |
| 9. #424×C71 | C2 | semidirect |
| 14. C2×#11765854 | C22 | semidirect |
| 17. C2×D568 | C22 | semidirect |
| 18. #14556125 | C22 | semidirect |
| 19. #14556116 | C22 | semidirect |
| 22. C4×D284 | C22 | semidirect |
| 26. #14556053 | C22 | semidirect |
| 27. #14556050 | C22 | semidirect |
| 28. #14556050 | C22 | semidirect |
| 32. C4⋊C8×C71 | C22 | semidirect |
| 44. C2×D284 | D4 | semidirect |
| 122. C71 | #3041 | semidirect |
| 129. #424 | D71 | semidirect |
| 151. C4⋊C8 | C2×D71 | semidirect |