Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22610028 | C2 | semidirect |
| 4. #22607816 | C2 | semidirect |
| 8. #17988526 | C4 | semidirect |
| 9. #17988523 | C4 | semidirect |
| 10. #17988517 | C4 | semidirect |
| 12. #17988512 | C4 | semidirect |
| 189. C73 | #9012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613190 | 2 |
| #22610028 | 2 |
| C4×#14556506 | 2 |
| #22607816 | 2 |
| C73×#2975 | 2 |
| #9012 | 73 |