Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C22×C71 | C23×C4 |
| Fitting | #386×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #386 | D71 |
| hypocenter | C71 | #2372 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17985903 | C2 | semidirect |
| 3. #17985893 | C2 | semidirect |
| 4. #17985887 | C2 | semidirect |
| 6. C22⋊C4×Dic71 | C2 | semidirect |
| 7. C4×C22⋊Dic71 | C2 | semidirect |
| 8. #17985844 | C2 | semidirect |
| 12. #14556115 | C4 | semidirect |
| 34. C2×Dic142 | C2×C4 | semidirect |
| 44. C22⋊Dic71 | C2×C4 | semidirect |
| 45. C22⋊Dic71 | C2×C4 | semidirect |
| 49. C4×Dic71 | C2×C4 | semidirect |
| 128. C71 | #2372 | semidirect |