Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 456 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. #22626820 | C2 | semidirect |
| 2. #22625322 | C2 | semidirect |
| 3. #22625320 | C2 | semidirect |
| 4. #22625292 | C2 | semidirect |
| 5. #22624788 | C2 | semidirect |
| 6. #22624754 | C2 | semidirect |
| 22. #17988963 | C4 | semidirect |
| 23. #17988937 | C4 | semidirect |
| 24. #17988934 | C4 | semidirect |
| 28. #492×C73 | C4 | semidirect |
| 186. C73 | #9281 | semidirect |
| 190. #492 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626820 | 2 |
| #22625322 | 2 |
| #22625320 | 2 |
| #22625292 | 2 |
| #22624788 | 2 |
| #22624754 | 2 |
| #22620861 | 2 |
| #9281 | 73 |