Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
544 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 2. #22625555 | C2 | semidirect |
| 3. #22625543 | C2 | semidirect |
| 139. C73 | #17991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626839 | 2 |
| #22625555 | 2 |
| #22625543 | 2 |
| #22625494 | 2 |
| #22625295 | 2 |
| #22625145 | 2 |
| #22620518 | 2 |
| #17991 | 73 |