Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. #22626839 | C2 | semidirect |
| 2. #22625325 | C2 | semidirect |
| 5. #22624788 | C2 | semidirect |
| 6. #22624754 | C2 | semidirect |
| 22. #17988961 | C4 | semidirect |
| 23. #17988937 | C4 | semidirect |
| 24. #17988934 | C4 | semidirect |
| 28. #494×C73 | C4 | semidirect |
| 175. C73 | #9282 | semidirect |
| 178. #494 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626839 | 2 |
| #22625325 | 2 |
| #22625322 | 2 |
| #22625292 | 2 |
| #22624788 | 2 |
| #22624754 | 2 |
| #22620884 | 2 |
| #9282 | 73 |