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. #22599056 | C2 | semidirect |
| 4. #22598711 | C2 | semidirect |
| 5. #22588011 | C2 | semidirect |
| 6. #22587992 | C2 | semidirect |
| 7. #22587977 | C2 | semidirect |
| 8. #22587945 | C2 | semidirect |
| 9. #22587942 | C2 | semidirect |
| 10. #22586644 | C2 | semidirect |
| 11. C71×#1715 | C2 | semidirect |
| 16. #17986404 | C22 | semidirect |
| 18. #17986379 | C22 | semidirect |
| 23. #17986351 | C22 | semidirect |
| 24. #17986349 | C22 | semidirect |
| 28. #17986345 | C22 | semidirect |
| 36. #17985721 | C22 | semidirect |
| 37. C8×C71⋊C8 | C22 | semidirect |
| 38. #498×C71 | C22 | semidirect |
| 40. #492×C71 | C22 | semidirect |
| 42. #322×C71 | C22 | semidirect |
| 195. #1715 | D71 | semidirect |
| 199. C71 | #19749 | semidirect |
| 205. #498 | C2×D71 | semidirect |
| 212. #492 | C2×D71 | semidirect |
| 229. #322 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599086 | 2 |
| #22599056 | 2 |
| #22598791 | 2 |
| #22598711 | 2 |
| #22588011 | 2 |
| #22587992 | 2 |
| #22587977 | 2 |
| #22587945 | 2 |
| #22587942 | 2 |
| #22586644 | 2 |
| C71×#1715 | 2 |
| #19749 | 71 |