Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
620 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 23. #17989316 | C4 | semidirect |
| 25. #17989315 | C4 | semidirect |
| 29. #17989312 | C4 | semidirect |
| 38. #557×C73 | C4 | semidirect |
| 259. C73 | #8495 | semidirect |
| 268. #557 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626119 | 2 |
| #22625466 | 2 |
| #22625423 | 2 |
| #22625324 | 2 |
| #22624423 | 2 |
| #8495 | 73 |