Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1630 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 195 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. #22620305 | C2 | semidirect |
| 2. #22620030 | C2 | semidirect |
| 3. #22609110 | C2 | semidirect |
| 4. #22608645 | C2 | semidirect |
| 5. #22608374 | C2 | semidirect |
| 7. #17989144 | C22 | semidirect |
| 9. #17988933 | C22 | semidirect |
| 11. #17988867 | C22 | semidirect |
| 12. #17988792 | C22 | semidirect |
| 15. #17988644 | C22 | semidirect |
| 17. C4×#11924012 | C22 | semidirect |
| 18. #17988331 | C22 | semidirect |
| 19. D4⋊#10596831 | C22 | semidirect |
| 30. #14556591 | C23 | semidirect |
| 36. C4⋊#10596831 | C23 | semidirect |
| 43. C4×#10596831 | C23 | semidirect |
| 173. C73 | #18529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620305 | 2 |
| #22620030 | 2 |
| #22609110 | 2 |
| #22608645 | 2 |
| #22608374 | 2 |
| C2×D42×C73 | 2 |
| #18529 | 73 |