Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #22625689 | C2 | semidirect |
| 4. #22625688 | C2 | semidirect |
| 5. #22625021 | C2 | semidirect |
| 6. #22625018 | C2 | semidirect |
| 9. C22×#11924038 | C4 | semidirect |
| 14. #17989593 | C4 | semidirect |
| 18. #17989559 | C4 | semidirect |
| 21. #17989551 | C4 | semidirect |
| 22. #17989489 | C4 | semidirect |
| 23. #17989488 | C4 | semidirect |
| 29. #17988377 | C4 | semidirect |
| 30. #17988375 | C4 | semidirect |
| 31. #17988373 | C4 | semidirect |
| 32. #352×C73 | C4 | semidirect |
| 223. C73 | #12624 | semidirect |
| 243. #352 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626652 | 2 |
| #22626185 | 2 |
| #22625689 | 2 |
| #22625688 | 2 |
| #22625021 | 2 |
| #22625018 | 2 |
| #22611571 | 2 |
| #12624 | 73 |