Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
668 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 146 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. #22624752 | C2 | semidirect |
| 30. C22×Dic146 | C8 | semidirect |
| 179. C73 | #7575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625785 | 2 |
| C4×C22⋊#10596833 | 2 |
| #22624752 | 2 |
| C2×#17988492 | 2 |
| #7575 | 73 |