Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1296 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 517 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, socle | C22×C71 | C25 |
| Fitting | #543×C71 | C2 |
| hypercenter | #543 | D71 |
| hypocenter | C71 | C2×#543 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #543 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986625 | C2 | semidirect |
| 2. #17986624 | C2 | semidirect |
| 3. C22⋊Q8×D71 | C2 | semidirect |
| 5. #543×C71 | C2 | semidirect |
| 7. C2×Q8×D71 | C22 | semidirect |
| 9. #14556108 | C22 | semidirect |
| 10. #14556107 | C22 | semidirect |
| 11. #14556106 | C22 | semidirect |
| 12. #14556105 | C22 | semidirect |
| 13. #14556104 | C22 | semidirect |
| 14. C4⋊C4×D71 | C22 | semidirect |
| 19. C22⋊Q8×C71 | C22 | semidirect |
| 22. C23×D71 | Q8 | semidirect |
| 25. C2×Dic142 | C23 | semidirect |
| 31. C4⋊Dic71 | C23 | semidirect |
| 32. Dic71⋊C4 | C23 | semidirect |
| 36. C2×Q8×C71 | C23 | semidirect |
| 38. C4⋊C4×C71 | C23 | semidirect |
| 41. C23×C71 | C2×Q8 | semidirect |
| 47. C22×D71 | C2×Q8 | semidirect |
| 74. D71 | #543 | direct (N × H) |
| 76. C71 | C2×#543 | semidirect |
| 79. #543 | D71 | direct (N × H) |
| 90. C22⋊Q8 | C2×D71 | semidirect |
| 104. C2×Q8 | C22×D71 | semidirect |
| 112. C4⋊C4 | C22×D71 | semidirect |
| 124. C23 | Q8×D71 | semidirect |