Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
908 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22599078 | C2 | semidirect |
| 2. #22599059 | C2 | semidirect |
| 3. #22598790 | C2 | semidirect |
| 4. #22588008 | C2 | semidirect |
| 5. #22587976 | C2 | semidirect |
| 6. #22587961 | C2 | semidirect |
| 7. #22587931 | C2 | semidirect |
| 8. #22586643 | C2 | semidirect |
| 9. C71×#3138 | C2 | semidirect |
| 12. #17986402 | C22 | semidirect |
| 13. #17986397 | C22 | semidirect |
| 15. #17986376 | C22 | semidirect |
| 18. #17986373 | C22 | semidirect |
| 21. #17986349 | C22 | semidirect |
| 22. #17986347 | C22 | semidirect |
| 23. #17986346 | C22 | semidirect |
| 29. #17985721 | C22 | semidirect |
| 30. #17985720 | C22 | semidirect |
| 31. C8×C71⋊C8 | C22 | semidirect |
| 150. C71⋊C8 | AGL(1,ℤ/8) | semidirect |
| 176. #3138 | D71 | semidirect |
| 182. C71 | #19747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599078 | 2 |
| #22599059 | 2 |
| #22598790 | 2 |
| #22588008 | 2 |
| #22587976 | 2 |
| #22587961 | 2 |
| #22587931 | 2 |
| #22586643 | 2 |
| C71×#3138 | 2 |
| #19747 | 71 |