Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 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. #499×D71 | C2 | semidirect |
| 3. #22590583 | C2 | semidirect |
| 4. #22590582 | C2 | semidirect |
| 5. #22590581 | C2 | semidirect |
| 6. #22590580 | C2 | semidirect |
| 7. #357×D71 | C2 | semidirect |
| 8. #346×D71 | C2 | semidirect |
| 9. C71×#2244 | C2 | semidirect |
| 15. #17986401 | C22 | semidirect |
| 16. #17986400 | C22 | semidirect |
| 26. #17985801 | C22 | semidirect |
| 27. #17985800 | C22 | semidirect |
| 28. #17985799 | C22 | semidirect |
| 29. #17985775 | C22 | semidirect |
| 30. #17985774 | C22 | semidirect |
| 31. #499×C71 | C22 | semidirect |
| 33. #357×C71 | C22 | semidirect |
| 34. #346×C71 | C22 | semidirect |
| 155. D71 | #2244 | direct (N × H) |
| 162. #2244 | D71 | direct (N × H) |
| 165. C71 | C2×#2244 | semidirect |
| 175. #499 | C2×D71 | semidirect |
| 187. #357 | C2×D71 | semidirect |
| 190. #346 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D71 | 2 |
| #493×D71 | 2 |
| #22590583 | 2 |
| #22590582 | 2 |
| #22590581 | 2 |
| #22590580 | 2 |
| #357×D71 | 2 |
| #346×D71 | 2 |
| C71×#2244 | 2 |
| C2×#2244 | 71 |