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. #22625967 | C2 | semidirect |
| 2. #22625960 | C2 | semidirect |
| 3. #22625937 | C2 | semidirect |
| 5. #22625861 | C2 | semidirect |
| 20. #17988978 | C4 | semidirect |
| 21. #17988967 | C4 | semidirect |
| 22. #17988966 | C4 | semidirect |
| 23. #17988959 | C4 | semidirect |
| 25. #492×C73 | C4 | semidirect |
| 149. C73 | #23360 | semidirect |
| 159. #492 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625967 | 2 |
| #22625960 | 2 |
| #22625937 | 2 |
| #22625934 | 2 |
| #22625861 | 2 |
| #22620385 | 2 |
| #23360 | 73 |