Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 573 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 | C22×#41×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C22×#41 | D71 |
| hypocenter | C71 | C2×#550 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11765866 | C2 | semidirect |
| 2. #17986668 | C2 | direct (N × H) |
| 3. C2×#14556124 | C2 | semidirect |
| 4. C2×#14556102 | C2 | semidirect |
| 5. C2×#14556099 | C2 | semidirect |
| 6. C2×Q8×Dic71 | C2 | semidirect |
| 7. C2×C4×C22⋊D71 | C2 | semidirect |
| 8. C22×#41×C71 | C2 | semidirect |
| 10. C2×#11765866 | C22 | semidirect |
| 15. #14556124 | C22 | semidirect |
| 16. #14556102 | C22 | semidirect |
| 17. #14556099 | C22 | semidirect |
| 18. Q8×Dic71 | C22 | semidirect |
| 19. C4×C22⋊D71 | C22 | semidirect |
| 26. C2×#41×C71 | C22 | semidirect |
| 50. C2×Q8×C71 | D4 | semidirect |
| 67. Q8×C71 | C2×D4 | semidirect |
| 78. C2×Dic71 | #41 | semidirect |
| 100. Dic71 | C2×#41 | semidirect |
| 102. C2×C71 | #550 | semidirect |
| 108. C71 | C2×#550 | semidirect |
| 110. C22×#41 | D71 | semidirect |
| 120. C2×#41 | C2×D71 | semidirect |
| 142. C2×Q8 | C22⋊D71 | semidirect |
| 175. Q8 | C2×C22⋊D71 | semidirect |
| 211. C2 | #17986668 | direct (N × H) |