Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
426 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 98 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. #22624988 | C2 | semidirect |
| 4. #22624988 | C2 | semidirect |
| 14. #17988625 | C4 | semidirect |
| 15. #17988624 | C4 | semidirect |
| 16. #17988624 | C4 | semidirect |
| 22. #427×C73 | C4 | semidirect |
| 167. C73 | #12868 | semidirect |
| 176. #427 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626156 | 2 |
| #22625808 | 2 |
| #22624988 | 2 |
| #427×D73 | 2 |
| #12868 | 73 |