Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
282 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 7. #64408⋊C16 | C4 | semidirect |
| 9. #17989677 | C4 | semidirect |
| 26. #14556660 | C8 | semidirect |
| 34. #14556525 | C8 | semidirect |
| 36. #107×C73 | C8 | semidirect |
| 129. C73 | #7171 | semidirect |
| 155. #107 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64408⋊C16 | 2 |
| C2×#17989677 | 2 |
| #107×#64408 | 2 |
| #7171 | 73 |