Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. #22598829 | C2 | semidirect |
| 3. #22597192 | C2 | semidirect |
| 4. #22590397 | C2 | semidirect |
| 5. #22590383 | C2 | semidirect |
| 6. #22590098 | C2 | semidirect |
| 7. #22590060 | C2 | semidirect |
| 8. #22590048 | C2 | semidirect |
| 9. C22×SD32×C71 | C2 | semidirect |
| 19. #17986384 | C22 | semidirect |
| 20. #17986377 | C22 | semidirect |
| 26. Dic71⋊C16 | C22 | semidirect |
| 27. #17985804 | C22 | semidirect |
| 28. #17985803 | C22 | semidirect |
| 29. #17985801 | C22 | semidirect |
| 178. C22×SD32 | D71 | semidirect |
| 186. C71 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986435 | 2 |
| #22598829 | 2 |
| #22597192 | 2 |
| #22590397 | 2 |
| #22590383 | 2 |
| #22590098 | 2 |
| #22590060 | 2 |
| #22590048 | 2 |
| C22×SD32×C71 | 2 |
| #33586 | 71 |