Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #525×C71 | C2 |
| hypercenter | #525 | D71 |
| hypocenter | C71 | #2978 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986077 | C2 | semidirect |
| 2. #17986071 | C2 | semidirect |
| 3. #17986060 | C2 | semidirect |
| 4. #17985966 | C2 | semidirect |
| 5. #17985963 | C2 | semidirect |
| 8. C2×#11765849 | C22 | semidirect |
| 9. C22×C71⋊C8 | C22 | semidirect |
| 10. C4⋊(C71⋊C8) | C22 | semidirect |
| 14. C22⋊(C71⋊C8) | C22 | semidirect |
| 15. #14556039 | C22 | semidirect |
| 16. C4×C71⋊C8 | C22 | semidirect |
| 90. C71 | #2978 | semidirect |