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. #22599054 | C2 | semidirect |
| 2. #22598793 | C2 | semidirect |
| 3. #22598715 | C2 | semidirect |
| 4. #22588005 | C2 | semidirect |
| 5. #22587980 | C2 | semidirect |
| 6. #22587965 | C2 | semidirect |
| 7. #22587931 | C2 | semidirect |
| 8. #22586643 | C2 | semidirect |
| 9. C71×#3184 | C2 | semidirect |
| 13. #17986402 | C22 | semidirect |
| 19. #17986371 | C22 | semidirect |
| 21. #17986351 | C22 | semidirect |
| 24. #17986345 | C22 | semidirect |
| 29. #17985721 | C22 | semidirect |
| 30. #17985720 | C22 | semidirect |
| 31. C8×C71⋊C8 | C22 | semidirect |
| 33. #498×C71 | C22 | semidirect |
| 34. #493×C71 | C22 | semidirect |
| 35. #486×C71 | C22 | semidirect |
| 150. C71⋊C8 | AGL(1,ℤ/8) | semidirect |
| 173. #3184 | D71 | semidirect |
| 182. C71 | #19747 | semidirect |
| 188. #498 | C2×D71 | semidirect |
| 192. #493 | C2×D71 | semidirect |
| 201. #486 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599054 | 2 |
| #22598793 | 2 |
| #22598715 | 2 |
| #22588005 | 2 |
| #22587980 | 2 |
| #22587965 | 2 |
| #22587931 | 2 |
| #22586643 | 2 |
| C71×#3184 | 2 |
| #19747 | 71 |