Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22620934 | C2 | semidirect |
| 2. #22620317 | C2 | semidirect |
| 3. #22609237 | C2 | semidirect |
| 4. #22608555 | C2 | semidirect |
| 5. #22608529 | C2 | semidirect |
| 7. #17989144 | C22 | semidirect |
| 8. #17988982 | C22 | semidirect |
| 9. #17988946 | C22 | semidirect |
| 10. #17988946 | C22 | semidirect |
| 15. #17988644 | C22 | semidirect |
| 18. C4×#11924012 | C22 | semidirect |
| 19. #17988327 | C22 | semidirect |
| 20. #17988327 | C22 | semidirect |
| 33. #14556591 | C23 | semidirect |
| 44. #14556502 | C23 | semidirect |
| 45. #14556502 | C23 | semidirect |
| 189. C73 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620934 | 2 |
| #22620317 | 2 |
| #22609237 | 2 |
| #22608555 | 2 |
| #22608529 | 2 |
| C2×H(3,𝔽4)×C73 | 2 |
| #18997 | 73 |