Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
436 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 25. #17988869 | C4 | semidirect |
| 26. #17988798 | C4 | semidirect |
| 27. #17988797 | C4 | semidirect |
| 32. #475×C73 | C4 | semidirect |
| 201. C73 | #9166 | semidirect |
| 206. #475 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626832 | 2 |
| #22625703 | 2 |
| #22625405 | 2 |
| #22625315 | 2 |
| #22624824 | 2 |
| #22624783 | 2 |
| #22620063 | 2 |
| #9166 | 73 |