Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
822 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22599083 | C2 | semidirect |
| 2. #22599057 | C2 | semidirect |
| 4. #22598711 | C2 | semidirect |
| 5. #22588012 | C2 | semidirect |
| 6. #22587990 | C2 | semidirect |
| 7. #22587976 | C2 | semidirect |
| 8. #22587966 | C2 | semidirect |
| 9. #22587941 | C2 | semidirect |
| 10. #22586642 | C2 | semidirect |
| 11. C71×#1709 | C2 | semidirect |
| 16. #17986402 | C22 | semidirect |
| 17. #17986397 | C22 | semidirect |
| 22. #17986371 | C22 | semidirect |
| 24. #17986350 | C22 | semidirect |
| 25. #17986349 | C22 | semidirect |
| 36. #17985720 | C22 | semidirect |
| 37. #17985720 | C22 | semidirect |
| 38. #494×C71 | C22 | semidirect |
| 41. #486×C71 | C22 | semidirect |
| 42. C82×C71 | C22 | semidirect |
| 196. #1709 | D71 | semidirect |
| 199. C71 | #19749 | semidirect |
| 207. #494 | C2×D71 | semidirect |
| 220. #486 | C2×D71 | semidirect |
| 230. C82 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599083 | 2 |
| #22599057 | 2 |
| #22598791 | 2 |
| #22598711 | 2 |
| #22588012 | 2 |
| #22587990 | 2 |
| #22587976 | 2 |
| #22587966 | 2 |
| #22587941 | 2 |
| #22586642 | 2 |
| C71×#1709 | 2 |
| #19749 | 71 |