Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
852 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 169 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 | #386×C71 | C2 |
| hypercenter | #386 | D71 |
| hypocenter | C71 | #2436 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic142 | C2 | semidirect |
| 2. C2×#14556114 | C2 | semidirect |
| 4. #17985912 | C2 | semidirect |
| 5. #17985911 | C2 | semidirect |
| 6. #17985903 | C2 | semidirect |
| 7. #17985879 | C2 | semidirect |
| 8. #17985878 | C2 | semidirect |
| 9. #17985876 | C2 | semidirect |
| 10. C22⋊C4×Dic71 | C2 | semidirect |
| 11. #386×C71 | C2 | semidirect |
| 46. C2×Dic142 | D4 | semidirect |
| 136. C22×C71 | #124 | semidirect |
| 164. C71 | #2436 | semidirect |
| 174. #386 | D71 | semidirect |
| 305. C22 | #14556114 | semidirect |