Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
702 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 702 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 |
|---|---|---|
| 1. #22625694 | C2 | semidirect |
| 2. #22625398 | C2 | semidirect |
| 3. #22625323 | C2 | semidirect |
| 4. #22625304 | C2 | semidirect |
| 5. #22625263 | C2 | semidirect |
| 6. #22625255 | C2 | semidirect |
| 22. Q8×Dic146 | C4 | semidirect |
| 26. #17989302 | C4 | semidirect |
| 28. #17989252 | C4 | semidirect |
| 38. #556×C73 | C4 | semidirect |
| 281. C73 | #8413 | semidirect |
| 286. #556 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625694 | 2 |
| #22625398 | 2 |
| #22625323 | 2 |
| #22625304 | 2 |
| #22625263 | 2 |
| #22625255 | 2 |
| #22623945 | 2 |
| #8413 | 73 |