Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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. #22625690 | C2 | semidirect |
| 4. #22625033 | C2 | semidirect |
| 7. C2×#14556678 | C4 | semidirect |
| 10. #17989592 | C4 | semidirect |
| 13. #17989561 | C4 | semidirect |
| 15. C4×#11924036 | C4 | semidirect |
| 21. #17988385 | C4 | semidirect |
| 22. #17988384 | C4 | semidirect |
| 23. #355×C73 | C4 | semidirect |
| 161. C73 | #12633 | semidirect |
| 176. #355 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626655 | 2 |
| #22626203 | 2 |
| #22625690 | 2 |
| #22625033 | 2 |
| #22611613 | 2 |
| #12633 | 73 |