Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
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. #22620420 | C2 | semidirect |
| 3. #22618783 | C2 | semidirect |
| 4. #22611988 | C2 | semidirect |
| 5. #22611974 | C2 | semidirect |
| 6. #22611689 | C2 | semidirect |
| 7. #22611651 | C2 | semidirect |
| 8. #22611639 | C2 | semidirect |
| 9. C22×SD32×C73 | C2 | semidirect |
| 19. #17988972 | C22 | semidirect |
| 20. #17988965 | C22 | semidirect |
| 26. #17988405 | C22 | semidirect |
| 27. #17988392 | C22 | semidirect |
| 28. #17988391 | C22 | semidirect |
| 29. #17988389 | C22 | semidirect |
| 178. C22×SD32 | D73 | semidirect |
| 186. C73 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22620420 | 2 |
| #22618783 | 2 |
| #22611988 | 2 |
| #22611974 | 2 |
| #22611689 | 2 |
| #22611651 | 2 |
| #22611639 | 2 |
| C22×SD32×C73 | 2 |
| #33586 | 73 |