Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22599064 | C2 | semidirect |
| 2. #22597250 | C2 | semidirect |
| 3. #22590560 | C2 | semidirect |
| 4. #22590552 | C2 | semidirect |
| 5. #22590514 | C2 | semidirect |
| 6. #22590407 | C2 | semidirect |
| 7. #22590291 | C2 | semidirect |
| 8. #22590239 | C2 | semidirect |
| 9. #22590228 | C2 | semidirect |
| 10. #22590149 | C2 | semidirect |
| 15. #17986399 | C22 | semidirect |
| 16. #17986382 | C22 | semidirect |
| 24. #17986111 | C22 | semidirect |
| 25. #17986105 | C22 | semidirect |
| 30. #17985822 | C22 | semidirect |
| 31. #17985821 | C22 | semidirect |
| 32. #17985819 | C22 | semidirect |
| 33. #17985816 | C22 | semidirect |
| 34. #17985812 | C22 | semidirect |
| 37. #17985776 | C22 | semidirect |
| 210. C71 | #33690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599064 | 2 |
| #22597250 | 2 |
| #22590560 | 2 |
| #22590552 | 2 |
| #22590514 | 2 |
| #22590407 | 2 |
| #22590291 | 2 |
| #22590239 | 2 |
| #22590228 | 2 |
| #22590149 | 2 |
| C71×#2190 | 2 |
| #33690 | 71 |