Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22625363 | C2 | semidirect |
| 4. #22625240 | C2 | semidirect |
| 5. #22624821 | C2 | semidirect |
| 6. #22624786 | C2 | semidirect |
| 26. #17988874 | C4 | semidirect |
| 27. #17988868 | C4 | semidirect |
| 28. #17988867 | C4 | semidirect |
| 32. #476×C73 | C4 | semidirect |
| 221. C73 | #9307 | semidirect |
| 227. #476 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626794 | 2 |
| #22625801 | 2 |
| #22625363 | 2 |
| #22625240 | 2 |
| #22624821 | 2 |
| #22624786 | 2 |
| #22619729 | 2 |
| #9307 | 73 |