Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
672 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 157 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, socle | C23×C71 | C24 |
| Fitting | C22×C22⋊C4×C71 | C2 |
| hypercenter | C22×C22⋊C4 | D71 |
| hypocenter | C71 | #2561 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556107 | C2 | semidirect |
| 2. #17985924 | C2 | semidirect |
| 3. #17985911 | C2 | semidirect |
| 4. #17985893 | C2 | semidirect |
| 5. #17985862 | C2 | semidirect |
| 7. C4×C22⋊Dic71 | C2 | semidirect |
| 9. C22×Dic142 | C22 | semidirect |
| 11. C2×C4⋊Dic71 | C22 | semidirect |
| 12. C2×Dic71⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic71 | C22 | semidirect |
| 18. C71⋊#95 | C22 | semidirect |
| 19. C71⋊#95 | C22 | semidirect |
| 20. C71⋊#95 | C22 | semidirect |
| 111. C71 | #2561 | semidirect |