Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
704 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 1. #22625694 | C2 | semidirect |
| 2. #22625396 | C2 | semidirect |
| 3. #22625323 | C2 | semidirect |
| 4. #22625302 | C2 | semidirect |
| 5. #22625263 | C2 | semidirect |
| 6. #22625255 | C2 | semidirect |
| 22. #17989312 | C4 | semidirect |
| 23. #17989294 | C4 | semidirect |
| 24. #17989294 | C4 | semidirect |
| 38. #547×C73 | C4 | semidirect |
| 281. C73 | #8415 | semidirect |
| 290. #547 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625694 | 2 |
| #22625396 | 2 |
| #22625323 | 2 |
| #22625302 | 2 |
| #22625263 | 2 |
| #22625255 | 2 |
| #22623900 | 2 |
| #8415 | 73 |