Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
400 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 114 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. #22625144 | C2 | semidirect |
| 4. #22625134 | C2 | semidirect |
| 5. #22624771 | C2 | semidirect |
| 6. #22624771 | C2 | semidirect |
| 176. C73 | #8158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625162 | 2 |
| #22625144 | 2 |
| #22625134 | 2 |
| #22624771 | 2 |
| C2×#17988645 | 2 |
| #8158 | 73 |