Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1170 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 1. #22626834 | C2 | semidirect |
| 2. #22625201 | C2 | semidirect |
| 3. #22625190 | C2 | semidirect |
| 4. #22625170 | C2 | semidirect |
| 166. C73 | #17425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626834 | 2 |
| #22625201 | 2 |
| #22625190 | 2 |
| #22625170 | 2 |
| C2×#17989244 | 2 |
| #17425 | 73 |