Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
396 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22626168 | C2 | semidirect |
| 2. #22625813 | C2 | semidirect |
| 3. #22624902 | C2 | semidirect |
| 8. #17989484 | C22 | semidirect |
| 10. #17989455 | C22 | semidirect |
| 11. C22×D584 | C4 | semidirect |
| 14. #17988841 | C4 | semidirect |
| 19. #427×C73 | C4 | semidirect |
| 155. C73 | #11868 | semidirect |
| 165. #427 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626168 | 2 |
| #22625813 | 2 |
| #22624902 | 2 |
| #22619580 | 2 |
| #11868 | 73 |