Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×#17989506 | C2 | semidirect |
| 3. #22626241 | C2 | semidirect |
| 5. #22625011 | C2 | semidirect |
| 6. #22625000 | C2 | semidirect |
| 25. #17988863 | C4 | semidirect |
| 26. #17988862 | C4 | semidirect |
| 29. #17988859 | C4 | semidirect |
| 32. #473×C73 | C4 | semidirect |
| 224. C73 | #13069 | semidirect |
| 240. #473 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626899 | 2 |
| C2×#17989506 | 2 |
| #22626241 | 2 |
| #22625817 | 2 |
| #22625011 | 2 |
| #22625000 | 2 |
| #473×D73 | 2 |
| #13069 | 73 |