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. #22599060 | C2 | semidirect |
| 4. #22598711 | C2 | semidirect |
| 5. #22587996 | C2 | semidirect |
| 6. #22587981 | C2 | semidirect |
| 7. #22587968 | C2 | semidirect |
| 8. #22587947 | C2 | semidirect |
| 9. #22587939 | C2 | semidirect |
| 10. #22586644 | C2 | semidirect |
| 11. C71×#1722 | C2 | semidirect |
| 16. #17986397 | C22 | semidirect |
| 21. #17986372 | C22 | semidirect |
| 23. #17986351 | C22 | semidirect |
| 24. #17986349 | C22 | semidirect |
| 26. #17986347 | C22 | semidirect |
| 36. #17985721 | C22 | semidirect |
| 37. C8×C71⋊C8 | C22 | semidirect |
| 38. #500×C71 | C22 | semidirect |
| 39. #494×C71 | C22 | semidirect |
| 42. #322×C71 | C22 | semidirect |
| 192. #1722 | D71 | semidirect |
| 199. C71 | #19749 | semidirect |
| 204. #500 | C2×D71 | semidirect |
| 207. #494 | 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 |
|---|---|
| #22599083 | 2 |
| #22599060 | 2 |
| #22598787 | 2 |
| #22598711 | 2 |
| #22587996 | 2 |
| #22587981 | 2 |
| #22587968 | 2 |
| #22587947 | 2 |
| #22587939 | 2 |
| #22586644 | 2 |
| C71×#1722 | 2 |
| #19749 | 71 |