Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 21. #17988939 | C4 | semidirect |
| 22. #17988938 | C4 | semidirect |
| 23. #17988937 | C4 | semidirect |
| 26. #487×C73 | C4 | semidirect |
| 164. C73 | #9426 | semidirect |
| 171. #487 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626476 | 2 |
| #22625465 | 2 |
| #22625355 | 2 |
| #22625354 | 2 |
| #22624791 | 2 |
| #22620308 | 2 |
| #9426 | 73 |