Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
776 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22609919 | C2 | semidirect |
| 3. #22607929 | C2 | semidirect |
| 4. C73×#1460 | C2 | semidirect |
| 5. C23×D292 | C4 | semidirect |
| 9. #17988504 | C4 | semidirect |
| 13. #17988447 | C4 | semidirect |
| 15. #17988354 | C22 | semidirect |
| 19. #323×C73 | C22 | semidirect |
| 204. #1460 | D73 | semidirect |
| 206. C73 | #11873 | semidirect |
| 221. #323 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613287 | 2 |
| #22609919 | 2 |
| #22607929 | 2 |
| C73×#1460 | 2 |
| #11873 | 73 |