Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#17989474 | C2 | semidirect |
| 4. #22625735 | C2 | semidirect |
| 5. #22624992 | C2 | semidirect |
| 6. #22624991 | C2 | semidirect |
| 11. #17989629 | C4 | semidirect |
| 17. #17989501 | C4 | semidirect |
| 23. #17988392 | C4 | semidirect |
| 24. #17988390 | C4 | semidirect |
| 25. #17988388 | C4 | semidirect |
| 26. #357×C73 | C4 | semidirect |
| 167. C73 | #12642 | semidirect |
| 184. #357 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989629 | 2 |
| C2×#17989501 | 2 |
| C2×#17989474 | 2 |
| #22625735 | 2 |
| #22624992 | 2 |
| #22624991 | 2 |
| #22611635 | 2 |
| #12642 | 73 |