Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 11. #17989627 | C4 | semidirect |
| 17. #17989506 | C4 | semidirect |
| 23. #17988392 | C4 | semidirect |
| 24. #17988391 | C4 | semidirect |
| 25. #17988390 | C4 | semidirect |
| 26. #358×C73 | C4 | semidirect |
| 165. C73 | #12648 | semidirect |
| 182. #358 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989627 | 2 |
| C2×#17989506 | 2 |
| C2×#17989478 | 2 |
| #22625738 | 2 |
| #22625002 | 2 |
| #22624996 | 2 |
| #22611649 | 2 |
| #12648 | 73 |