Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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×#17989025 | C2 | semidirect |
| 2. C22×#14556532 | C2 | semidirect |
| 3. #22620412 | C2 | semidirect |
| 4. #22618782 | C2 | semidirect |
| 5. #22611985 | C2 | semidirect |
| 6. #22611965 | C2 | semidirect |
| 7. #22611691 | C2 | semidirect |
| 8. #22611636 | C2 | semidirect |
| 9. C73×#2140 | C2 | semidirect |
| 16. C2×#14556536 | C22 | semidirect |
| 17. C2×D1168 | C22 | semidirect |
| 22. #17988970 | C22 | semidirect |
| 23. #17988962 | C22 | semidirect |
| 25. #17988669 | C22 | semidirect |
| 28. #17988405 | C22 | semidirect |
| 29. #17988390 | C22 | semidirect |
| 30. #17988387 | C22 | semidirect |
| 34. #357×C73 | C22 | semidirect |
| 45. C2×D584 | D4 | semidirect |
| 189. #2140 | D73 | semidirect |
| 191. C73 | #33585 | semidirect |
| 216. #357 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989025 | 2 |
| C22×#14556532 | 2 |
| #22620412 | 2 |
| #22618782 | 2 |
| #22611985 | 2 |
| #22611965 | 2 |
| #22611691 | 2 |
| #22611636 | 2 |
| C73×#2140 | 2 |
| #33585 | 73 |