Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #385×C71 | C2 |
| hypercenter | #385 | D71 |
| hypocenter | C71 | #2463 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #385 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556106 | C2 | semidirect |
| 2. C2×C4×C22⋊D71 | C2 | semidirect |
| 3. #17985914 | C2 | semidirect |
| 4. #17985911 | C2 | semidirect |
| 6. #17985889 | C2 | semidirect |
| 7. #17985881 | C2 | semidirect |
| 8. #17985877 | C2 | semidirect |
| 9. #385×C71 | C2 | semidirect |
| 48. Dic71⋊C4 | D4 | semidirect |
| 134. C71 | #2463 | semidirect |
| 143. #385 | D71 | semidirect |