Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626159 | C2 | semidirect |
| 2. #22625617 | C2 | semidirect |
| 3. #22624918 | C2 | semidirect |
| 4. #22624917 | C2 | semidirect |
| 8. #17989482 | C22 | semidirect |
| 11. #17989461 | C22 | semidirect |
| 12. C2×D8×D73 | C4 | semidirect |
| 16. #17988823 | C4 | semidirect |
| 20. #107×D73 | C4 | semidirect |
| 22. #466×C73 | C4 | semidirect |
| 189. C73 | #11705 | semidirect |
| 200. #466 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626159 | 2 |
| #22625617 | 2 |
| #22624918 | 2 |
| #22624917 | 2 |
| #466×D73 | 2 |
| #11705 | 73 |