Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 2. #22625724 | C2 | semidirect |
| 4. #22625147 | C2 | semidirect |
| 5. #22624828 | C2 | semidirect |
| 6. #22624823 | C2 | semidirect |
| 10. #17989622 | C4 | semidirect |
| 12. D4×#10596833 | C4 | semidirect |
| 26. #17988334 | C4 | semidirect |
| 27. #17988332 | C4 | semidirect |
| 28. #17988331 | C4 | semidirect |
| 29. #331×C73 | C4 | semidirect |
| 188. C73 | #8257 | semidirect |
| 207. #331 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626653 | 2 |
| #22625724 | 2 |
| #22625311 | 2 |
| #22625147 | 2 |
| #22624828 | 2 |
| #22624823 | 2 |
| #22608577 | 2 |
| #8257 | 73 |