Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1030 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 226 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. #22626833 | C2 | semidirect |
| 2. #22626371 | C2 | semidirect |
| 3. #22625335 | C2 | semidirect |
| 4. #22625322 | C2 | semidirect |
| 5. #22625312 | C2 | semidirect |
| 6. #22625304 | C2 | semidirect |
| 21. #17989322 | C4 | semidirect |
| 22. #17989298 | C4 | semidirect |
| 23. #17989259 | C4 | semidirect |
| 31. Q82×C73 | C4 | semidirect |
| 191. C73 | #17550 | semidirect |
| 193. Q82 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626833 | 2 |
| #22626371 | 2 |
| #22625335 | 2 |
| #22625322 | 2 |
| #22625312 | 2 |
| #22625304 | 2 |
| #22624017 | 2 |
| #17550 | 73 |