Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 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 | C2×2−1+4×C71 | C2 |
| hypercenter | C2×2−1+4 | D71 |
| hypocenter | C71 | #3486 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D71 | C2 | semidirect |
| 2. Q8×C22⋊D71 | C2 | semidirect |
| 3. #17986656 | C2 | semidirect |
| 4. #17986570 | C2 | semidirect |
| 5. #17986506 | C2 | semidirect |
| 6. #17986477 | C2 | semidirect |
| 7. C2×2−1+4×C71 | C2 | semidirect |
| 12. #14556126 | C22 | semidirect |
| 13. #14556115 | C22 | semidirect |
| 15. #14556107 | C22 | semidirect |
| 19. Q8×Dic71 | C22 | semidirect |
| 24. C2×#41×C71 | C22 | semidirect |
| 26. C22×Q8×C71 | C22 | semidirect |
| 44. C2×Q8×C71 | D4 | semidirect |
| 78. C2×D71 | 2−1+4 | semidirect |
| 89. C71 | #3486 | semidirect |
| 90. C2×2−1+4 | D71 | semidirect |
| 99. C2×#41 | C2×D71 | semidirect |
| 104. C22×Q8 | C2×D71 | semidirect |
| 123. C2×Q8 | C22⋊D71 | semidirect |