Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C2×#120×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#120 | D71 |
| hypocenter | C71 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986742 | C2 | direct (N × H) |
| 2. C2×#14556115 | C2 | semidirect |
| 3. C2×#14556114 | C2 | semidirect |
| 4. C2×#14556097 | C2 | semidirect |
| 5. C2×#14556096 | C2 | semidirect |
| 6. C2×#120×C71 | C2 | semidirect |
| 7. C24×D71 | C22 | semidirect |
| 8. C22×Dic142 | C22 | semidirect |
| 10. #14556115 | C22 | semidirect |
| 11. #14556114 | C22 | semidirect |
| 12. #14556097 | C22 | semidirect |
| 13. #14556096 | C22 | semidirect |
| 14. C2×C22⋊Dic71 | C22 | semidirect |
| 15. C2×C22⋊Dic71 | C22 | semidirect |
| 16. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic71 | C22 | semidirect |
| 18. C25×C71 | C22 | semidirect |
| 20. #120×C71 | C22 | semidirect |
| 21. C2×C22⋊C4×C71 | C22 | semidirect |
| 24. C23×D71 | C23 | semidirect |
| 26. C2×Dic142 | C23 | semidirect |
| 30. C22⋊Dic71 | C23 | semidirect |
| 31. C22⋊Dic71 | C23 | semidirect |
| 32. (C2×D71)⋊C4 | C23 | semidirect |
| 33. C4×Dic71 | C23 | semidirect |
| 37. C24×C71 | C23 | semidirect |
| 41. C22⋊C4×C71 | C23 | semidirect |
| 76. C2×C71 | H(3,𝔽4) | semidirect |
| 80. C71 | C2×H(3,𝔽4) | semidirect |
| 86. C2×#120 | D71 | semidirect |
| 88. C25 | C2×D71 | semidirect |
| 96. #120 | C2×D71 | semidirect |
| 100. C2×C22⋊C4 | C2×D71 | semidirect |
| 108. C24 | C22×D71 | semidirect |
| 120. C22⋊C4 | C22×D71 | semidirect |
| 157. C2 | #17986742 | direct (N × H) |