Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 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 | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #379×C71 | C2 |
| hypercenter | #379 | D71 |
| hypocenter | C71 | #2849 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic71 | C2 | semidirect |
| 2. C2×#14556112 | C2 | semidirect |
| 4. #17985876 | C2 | semidirect |
| 5. #17985874 | C2 | semidirect |
| 6. #17985860 | C2 | semidirect |
| 7. #379×C71 | C2 | semidirect |
| 16. C2×C4⋊Dic71 | C22 | semidirect |
| 19. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 20. C71⋊#95 | C22 | semidirect |
| 34. C22×Dic71 | D4 | semidirect |
| 84. C22×C71 | #123 | semidirect |
| 102. C71 | #2849 | semidirect |
| 109. #379 | D71 | semidirect |
| 189. C22 | #14556112 | semidirect |