Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #22625405 | C2 | semidirect |
| 4. #22625315 | C2 | semidirect |
| 5. #22624824 | C2 | semidirect |
| 6. #22624783 | C2 | semidirect |
| 25. #17988864 | C4 | semidirect |
| 26. #17988793 | C4 | semidirect |
| 27. #17988792 | C4 | semidirect |
| 32. #474×C73 | C4 | semidirect |
| 218. C73 | #9165 | semidirect |
| 223. #474 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626791 | 2 |
| #22625701 | 2 |
| #22625405 | 2 |
| #22625315 | 2 |
| #22624824 | 2 |
| #22624783 | 2 |
| #22620032 | 2 |
| #9165 | 73 |