Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
458 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626109 | C2 | semidirect |
| 4. #22625445 | C2 | semidirect |
| 5. #22624827 | C2 | semidirect |
| 6. #22624800 | C2 | semidirect |
| 26. #17988872 | C4 | semidirect |
| 27. #17988868 | C4 | semidirect |
| 28. #17988864 | C4 | semidirect |
| 32. #475×C73 | C4 | semidirect |
| 218. C73 | #9319 | semidirect |
| 224. #475 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626855 | 2 |
| #22626109 | 2 |
| #22625806 | 2 |
| #22625445 | 2 |
| #22624827 | 2 |
| #22624800 | 2 |
| #22619741 | 2 |
| #9319 | 73 |