Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #418×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #418 | D71 |
| hypocenter | C71 | #2948 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #418 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986474 | C2 | semidirect |
| 3. #17986473 | C2 | semidirect |
| 4. #17986108 | C2 | semidirect |
| 5. #17986079 | C2 | semidirect |
| 6. #17986035 | C2 | semidirect |
| 7. #17986005 | C2 | semidirect |
| 8. #17985957 | C2 | semidirect |
| 9. #418×C71 | C2 | semidirect |
| 11. C2×#11765850 | C4 | semidirect |
| 17. D4×Dic71 | C22 | semidirect |
| 18. #14556090 | C22 | semidirect |
| 23. #14556061 | C22 | semidirect |
| 24. #14556059 | C22 | semidirect |
| 25. #14556050 | C22 | semidirect |
| 26. #14556038 | C22 | semidirect |
| 27. C8×Dic71 | C22 | semidirect |
| 31. #102×C71 | C22 | semidirect |
| 35. C2×D284 | C2×C4 | semidirect |
| 39. #11765850 | C2×C4 | semidirect |
| 40. #11765850 | C2×C4 | semidirect |
| 41. C2×C71⋊C8 | C2×C4 | semidirect |
| 55. C2×D4×C71 | C2×C4 | semidirect |
| 109. C71 | #2948 | semidirect |
| 117. #418 | D71 | semidirect |
| 138. #102 | C2×D71 | semidirect |
| 149. C2×D4 | C4×D71 | semidirect |