Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22627092 | C2 | semidirect |
| 4. #22627009 | C2 | semidirect |
| 8. C2×#14556688 | C4 | semidirect |
| 9. C2×#14556687 | C4 | semidirect |
| 12. C2×#14556686 | C4 | semidirect |
| 13. C22×#11924040 | C4 | semidirect |
| 15. #17989686 | C4 | semidirect |
| 16. #17989685 | C4 | semidirect |
| 143. C73 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989708 | 2 |
| #22627107 | 2 |
| #22627092 | 2 |
| #22627009 | 2 |
| #22625689 | 2 |
| #12613 | 73 |