Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
904 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22627115 | C2 | semidirect |
| 2. #22627113 | C2 | semidirect |
| 3. #22627105 | C2 | semidirect |
| 4. #22627105 | C2 | semidirect |
| 6. #17989706 | C22 | semidirect |
| 7. #17989706 | C22 | semidirect |
| 259. C73 | #12686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627115 | 2 |
| #22627113 | 2 |
| #22627105 | 2 |
| C2×#17989666 | 2 |
| #12686 | 73 |