Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
404 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 29. #14556652 | Q8 | semidirect |
| 163. C73 | #13301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625798 | 2 |
| #22625684 | 2 |
| #22625029 | 2 |
| #22625028 | 2 |
| #22615144 | 2 |
| #13301 | 73 |