Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Fitting | #433×C71 | C2 |
| hypercenter | #433 | D71 |
| hypocenter | C71 | #2977 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986072 | C2 | semidirect |
| 3. #17986069 | C2 | semidirect |
| 4. C8×D284 | C2 | semidirect |
| 5. #17986064 | C2 | semidirect |
| 6. #17986060 | C2 | semidirect |
| 7. #17985964 | C2 | semidirect |
| 8. C22⋊C8×D71 | C2 | semidirect |
| 9. #433×C71 | C2 | semidirect |
| 12. C2×#11765848 | C22 | semidirect |
| 15. C2×C8×D71 | C22 | semidirect |
| 22. C4⋊(C71⋊C8) | C22 | semidirect |
| 26. (C2×D71)⋊C8 | C22 | semidirect |
| 27. (C2×D71)⋊C8 | C22 | semidirect |
| 28. #14556039 | C22 | semidirect |
| 29. C4×C71⋊C8 | C22 | semidirect |
| 31. C4⋊C8×C71 | C22 | semidirect |
| 33. #97×C71 | C22 | semidirect |
| 34. C4×C8×C71 | C22 | semidirect |
| 115. C71 | #2977 | semidirect |
| 122. #433 | D71 | semidirect |
| 139. C4⋊C8 | C2×D71 | semidirect |
| 147. #97 | C2×D71 | semidirect |
| 149. C4×C8 | C2×D71 | semidirect |