Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. #22625670 | C2 | semidirect |
| 3. #22625669 | C2 | semidirect |
| 5. #22624814 | C2 | semidirect |
| 6. #22624812 | C2 | semidirect |
| 8. C2×#14556679 | C4 | semidirect |
| 14. #17989594 | C4 | semidirect |
| 15. #17989562 | C4 | semidirect |
| 18. #17989552 | C4 | semidirect |
| 24. #17989441 | C4 | semidirect |
| 25. #17989439 | C4 | semidirect |
| 29. #17988324 | C4 | semidirect |
| 30. #17988322 | C4 | semidirect |
| 31. #17988320 | C4 | semidirect |
| 32. #328×C73 | C4 | semidirect |
| 233. C73 | #8239 | semidirect |
| 255. #328 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626647 | 2 |
| #22625670 | 2 |
| #22625669 | 2 |
| #22625309 | 2 |
| #22624814 | 2 |
| #22624812 | 2 |
| #22608421 | 2 |
| #8239 | 73 |