Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1276 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 260 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. #22625843 | C2 | semidirect |
| 3. #22625629 | C2 | semidirect |
| 12. #17989065 | C4 | semidirect |
| 13. #17989061 | C4 | semidirect |
| 16. #117×D73 | C4 | semidirect |
| 18. #519×C73 | C4 | semidirect |
| 161. C73 | #20710 | semidirect |
| 165. #519 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989568 | 2 |
| #22625843 | 2 |
| #22625629 | 2 |
| #22623133 | 2 |
| #20710 | 73 |