Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
688 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 154 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. #22625966 | C2 | semidirect |
| 2. #22625961 | C2 | semidirect |
| 3. #22625937 | C2 | semidirect |
| 5. #22625861 | C2 | semidirect |
| 20. #17988980 | C4 | semidirect |
| 21. #17988966 | C4 | semidirect |
| 22. #17988961 | C4 | semidirect |
| 23. #17988960 | C4 | semidirect |
| 25. #494×C73 | C4 | semidirect |
| 149. C73 | #23360 | semidirect |
| 157. #494 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625966 | 2 |
| #22625961 | 2 |
| #22625937 | 2 |
| #22625933 | 2 |
| #22625861 | 2 |
| #22620389 | 2 |
| #23360 | 73 |