Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×#17989482 | C2 | semidirect |
| 2. #22625617 | C2 | semidirect |
| 3. #22624920 | C2 | semidirect |
| 4. #22624918 | C2 | semidirect |
| 12. C2×#14556613 | C4 | semidirect |
| 15. #17988829 | C4 | semidirect |
| 17. #17988824 | C4 | semidirect |
| 22. #427×C73 | C4 | semidirect |
| 179. C73 | #11703 | semidirect |
| 191. #427 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989482 | 2 |
| #22625617 | 2 |
| #22624920 | 2 |
| #22624918 | 2 |
| #22619513 | 2 |
| #11703 | 73 |