Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
472 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #390×C71 | C2 |
| hypercenter | #390 | D71 |
| hypocenter | C71 | #2784 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17985938 | C2 | semidirect |
| 2. #17985922 | C2 | semidirect |
| 3. #17985919 | C2 | semidirect |
| 4. #17985911 | C2 | semidirect |
| 5. #17985883 | C2 | semidirect |
| 7. #17985871 | C2 | semidirect |
| 8. #17985857 | C2 | semidirect |
| 50. C2×D4×C71 | Q8 | semidirect |
| 119. C71 | #2784 | semidirect |
| 155. C2×D4 | Dic142 | semidirect |