Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 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. C2×#17989023 | C2 | semidirect |
| 2. #22620412 | C2 | semidirect |
| 3. #22618783 | C2 | semidirect |
| 4. #22611984 | C2 | semidirect |
| 5. #22611964 | C2 | semidirect |
| 6. #22611689 | C2 | semidirect |
| 7. #22611647 | C2 | semidirect |
| 8. #22611639 | C2 | semidirect |
| 9. C22×D16×C73 | C2 | semidirect |
| 15. C2×#14556535 | C22 | semidirect |
| 16. C2×#14556532 | C22 | semidirect |
| 19. #17988970 | C22 | semidirect |
| 20. #17988962 | C22 | semidirect |
| 22. D8×Dic73 | C22 | semidirect |
| 26. #17988405 | C22 | semidirect |
| 27. #17988392 | C22 | semidirect |
| 28. #17988389 | C22 | semidirect |
| 29. #17988388 | C22 | semidirect |
| 70. C2×D8×C73 | D4 | semidirect |
| 183. C22×D16 | D73 | semidirect |
| 191. C73 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22620412 | 2 |
| #22618783 | 2 |
| #22611984 | 2 |
| #22611964 | 2 |
| #22611689 | 2 |
| #22611647 | 2 |
| #22611639 | 2 |
| C22×D16×C73 | 2 |
| #33585 | 73 |