Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 12. #17989444 | C4 | semidirect |
| 161. C73 | #8225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625648 | 2 |
| C2×#17989444 | 2 |
| #22624807 | 2 |
| #22612490 | 2 |
| #8225 | 73 |