Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. #22626303 | C2 | semidirect |
| 2. #22625861 | C2 | semidirect |
| 3. #22624908 | C2 | semidirect |
| 5. #22624904 | C2 | semidirect |
| 17. #17988971 | C4 | semidirect |
| 22. #17988698 | C4 | semidirect |
| 23. #17988693 | C4 | semidirect |
| 26. #499×C73 | C4 | semidirect |
| 147. C73 | #11836 | semidirect |
| 149. #499 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626303 | 2 |
| #22625861 | 2 |
| #22624908 | 2 |
| #22624906 | 2 |
| #22624904 | 2 |
| #22624902 | 2 |
| #22620662 | 2 |
| #11836 | 73 |