Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1306 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 232 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. #22626607 | C2 | semidirect |
| 2. #22625412 | C2 | semidirect |
| 3. #22625392 | C2 | semidirect |
| 5. #17989608 | C22 | semidirect |
| 6. #17989607 | C22 | semidirect |
| 11. C4×#11924037 | C22 | semidirect |
| 12. #17989443 | C22 | semidirect |
| 29. #14556646 | C23 | semidirect |
| 185. C73 | #17666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626607 | 2 |
| #22625412 | 2 |
| #22625392 | 2 |
| C22×#14556580 | 2 |
| #17666 | 73 |