Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | C2×C4×D4×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×C4×D4 | D71 |
| hypocenter | C71 | #2328 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D284 | C2 | semidirect |
| 3. #17985902 | C2 | semidirect |
| 4. #17985900 | C2 | semidirect |
| 5. #17985878 | C2 | semidirect |
| 6. #17985875 | C2 | semidirect |
| 7. #17985864 | C2 | semidirect |
| 8. #17985845 | C2 | semidirect |
| 9. C2×C4×D4×C71 | C2 | semidirect |
| 13. #14556124 | C4 | semidirect |
| 33. C2×D284 | C2×C4 | semidirect |
| 36. C2×C22⋊D71 | C2×C4 | semidirect |
| 47. C4×Dic71 | C2×C4 | semidirect |
| 51. C2×D4×C71 | C2×C4 | semidirect |
| 60. C42×C71 | D4 | semidirect |
| 124. C71 | #2328 | semidirect |
| 127. C2×C4×D4 | D71 | semidirect |
| 164. C2×D4 | C4×D71 | semidirect |
| 184. C42 | C22⋊D71 | semidirect |