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. #22599086 | C2 | semidirect |
| 2. #22599061 | C2 | semidirect |
| 4. #22598711 | C2 | semidirect |
| 5. #22588009 | C2 | semidirect |
| 6. #22587994 | C2 | semidirect |
| 7. #22587980 | C2 | semidirect |
| 8. #22587969 | C2 | semidirect |
| 9. #22587946 | C2 | semidirect |
| 10. #22586642 | C2 | semidirect |
| 11. C71×#1708 | C2 | semidirect |
| 16. #17986402 | C22 | semidirect |
| 18. #17986379 | C22 | semidirect |
| 22. #17986373 | C22 | semidirect |
| 24. #17986351 | C22 | semidirect |
| 27. #17986346 | C22 | semidirect |
| 36. #17985720 | C22 | semidirect |
| 37. #17985720 | C22 | semidirect |
| 38. #498×C71 | C22 | semidirect |
| 40. #487×C71 | C22 | semidirect |
| 42. C82×C71 | C22 | semidirect |
| 197. #1708 | D71 | semidirect |
| 199. C71 | #19749 | semidirect |
| 205. #498 | C2×D71 | semidirect |
| 215. #487 | 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 |
|---|---|
| #22599086 | 2 |
| #22599061 | 2 |
| #22598787 | 2 |
| #22598711 | 2 |
| #22588009 | 2 |
| #22587994 | 2 |
| #22587980 | 2 |
| #22587969 | 2 |
| #22587946 | 2 |
| #22586642 | 2 |
| C71×#1708 | 2 |
| #19749 | 71 |