Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
206 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 9. #17989449 | C4 | semidirect |
| 13. #17988363 | C4 | semidirect |
| 14. #346×C73 | C4 | semidirect |
| 89. C73 | #7221 | semidirect |
| 96. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625853 | 2 |
| #22625487 | 2 |
| #22611732 | 2 |
| #7221 | 73 |