Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
574 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 27. #17988325 | C4 | semidirect |
| 28. #17988324 | C4 | semidirect |
| 29. #17988323 | C4 | semidirect |
| 30. #328×C73 | C4 | semidirect |
| 277. C73 | #8867 | semidirect |
| 300. #328 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626424 | 2 |
| #22625916 | 2 |
| #22625880 | 2 |
| #22625117 | 2 |
| #22624805 | 2 |
| #22624768 | 2 |
| #328×D73 | 2 |
| #8867 | 73 |