Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 4. #17989592 | C4 | semidirect |
| 8. #17989523 | C4 | semidirect |
| 9. #17989498 | C4 | semidirect |
| 14. #17988380 | C4 | semidirect |
| 15. #353×C73 | C4 | semidirect |
| 127. C73 | #7503 | semidirect |
| 139. #353 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626223 | 2 |
| #22626069 | 2 |
| #22611593 | 2 |
| #7503 | 73 |