Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #473×C71 | C2 |
| socle | C2×C71 | C2×#121 |
| hypercenter | #473 | D71 |
| hypocenter | C71 | #3067 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #473 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986798 | C2 | semidirect |
| 2. C2×#14556151 | C2 | semidirect |
| 3. #131×D71 | C2 | semidirect |
| 4. #17986271 | C2 | semidirect |
| 5. #17986270 | C2 | semidirect |
| 6. #17986269 | C2 | semidirect |
| 7. #17986265 | C2 | semidirect |
| 8. #17986264 | C2 | semidirect |
| 9. #108×D71 | C2 | semidirect |
| 10. #17985982 | C2 | semidirect |
| 11. #473×C71 | C2 | semidirect |
| 25. C2×#11765852 | C22 | semidirect |
| 26. C2×D568 | C22 | semidirect |
| 37. #14556064 | C22 | semidirect |
| 38. #14556063 | C22 | semidirect |
| 39. #14556047 | C22 | semidirect |
| 40. #14556044 | C22 | semidirect |
| 41. #14556044 | C22 | semidirect |
| 43. C2×Q16×C71 | C22 | semidirect |
| 45. #108×C71 | C22 | semidirect |
| 46. #101×C71 | C22 | semidirect |
| 167. C71 | #3067 | semidirect |
| 172. #473 | D71 | semidirect |
| 193. C2×Q16 | C2×D71 | semidirect |
| 209. #108 | C2×D71 | semidirect |
| 211. #101 | C2×D71 | semidirect |