Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 3. #22625903 | C2 | semidirect |
| 4. #22625018 | C2 | semidirect |
| 19. #17988381 | C4 | semidirect |
| 20. #17988380 | C4 | semidirect |
| 21. #353×C73 | C4 | semidirect |
| 150. C73 | #12969 | semidirect |
| 164. #353 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626816 | 2 |
| #22625934 | 2 |
| #22625903 | 2 |
| #22625018 | 2 |
| #22611593 | 2 |
| #12969 | 73 |