Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 13. #17989506 | C4 | semidirect |
| 14. #17989500 | C4 | semidirect |
| 20. #17988695 | C4 | semidirect |
| 21. #17988694 | C4 | semidirect |
| 22. #17988693 | C4 | semidirect |
| 28. #441×C73 | C4 | semidirect |
| 181. C73 | #12648 | semidirect |
| 191. #441 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#362 | 2 |
| #22626241 | 2 |
| #22626148 | 2 |
| #22625737 | 2 |
| #22625004 | 2 |
| #22624995 | 2 |
| #441×D73 | 2 |
| #12648 | 73 |