Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22619061 | C2 | semidirect |
| 3. C4×#14556519 | C2 | semidirect |
| 4. #22608348 | C2 | semidirect |
| 5. #22607820 | C2 | semidirect |
| 6. #22607764 | C2 | semidirect |
| 7. C73×#1962 | C2 | semidirect |
| 10. #17988879 | C4 | semidirect |
| 11. #17988874 | C4 | semidirect |
| 12. #17988784 | C4 | semidirect |
| 13. #17988779 | C4 | semidirect |
| 179. Dic146 | #104 | semidirect |
| 219. #1962 | D73 | semidirect |
| 224. C73 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619985 | 2 |
| #22619061 | 2 |
| C4×#14556519 | 2 |
| #22608348 | 2 |
| #22607820 | 2 |
| #22607764 | 2 |
| C73×#1962 | 2 |
| #8970 | 73 |