Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #423×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #423 | D71 |
| hypocenter | C71 | #3036 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556156 | C2 | semidirect |
| 2. #17986549 | C2 | semidirect |
| 3. C2×C4×D284 | C2 | semidirect |
| 4. #17986215 | C2 | semidirect |
| 5. #17986205 | C2 | semidirect |
| 6. #17986195 | C2 | semidirect |
| 7. #17986001 | C2 | semidirect |
| 8. #423×C71 | C2 | semidirect |
| 15. #14556128 | C22 | semidirect |
| 16. #14556125 | C22 | semidirect |
| 17. #14556116 | C22 | semidirect |
| 28. #14556053 | C22 | semidirect |
| 29. #14556050 | C22 | semidirect |
| 32. C4⋊C8×C71 | C22 | semidirect |
| 33. C4⋊C8×C71 | C22 | semidirect |
| 42. C2×D284 | D4 | semidirect |
| 118. C4×C71 | AGL(1,ℤ/8) | semidirect |
| 130. C71 | #3036 | semidirect |
| 137. #423 | D71 | semidirect |
| 160. C4⋊C8 | C2×D71 | semidirect |
| 161. C4⋊C8 | C2×D71 | semidirect |
| 250. C4 | #14556156 | semidirect |