Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator | C2×C71 | C24×C4 |
| Fitting | #519×C71 | C2 |
| socle | C22×C71 | C25 |
| hypercenter | #519 | D71 |
| hypocenter | C71 | C2×#519 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986477 | C2 | semidirect |
| 3. #17986476 | C2 | semidirect |
| 4. #17986475 | C2 | semidirect |
| 5. C4×Q8×D71 | C2 | semidirect |
| 7. #519×C71 | C2 | semidirect |
| 9. C2×Q8×D71 | C4 | semidirect |
| 13. Q8×Dic71 | C22 | semidirect |
| 14. C4×Dic142 | C22 | semidirect |
| 15. #14556093 | C22 | semidirect |
| 24. C4×Q8×C71 | C22 | semidirect |
| 27. C2×Dic142 | C2×C4 | semidirect |
| 30. Q8×D71 | C2×C4 | semidirect |
| 42. C2×Q8×C71 | C2×C4 | semidirect |
| 80. D71 | #519 | direct (N × H) |
| 82. C71 | C2×#519 | semidirect |
| 87. #519 | D71 | direct (N × H) |
| 99. C4×Q8 | C2×D71 | semidirect |
| 113. C2×Q8 | C4×D71 | semidirect |