Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
728 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #22611584 | C2 | semidirect |
| 4. #22610483 | C2 | semidirect |
| 7. #17989337 | C4 | semidirect |
| 8. #17989323 | C4 | semidirect |
| 197. C73 | #12771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624345 | 2 |
| #22611616 | 2 |
| #22611584 | 2 |
| #22610483 | 2 |
| C73×#1884 | 2 |
| #12771 | 73 |