Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 7. #17989509 | C4 | semidirect |
| 9. C8×#10596833 | C4 | semidirect |
| 25. #14556523 | C8 | semidirect |
| 35. #108×C73 | C8 | semidirect |
| 101. C73 | #7180 | semidirect |
| 122. #108 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989509 | 2 |
| #22625134 | 2 |
| #22609813 | 2 |
| #7180 | 73 |