Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
296 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 10. #17989510 | C4 | semidirect |
| 11. #17989509 | C4 | semidirect |
| 18. #17988363 | C4 | semidirect |
| 19. C16×Dic73 | C4 | semidirect |
| 20. C16×Dic73 | C4 | semidirect |
| 21. #346×C73 | C4 | semidirect |
| 117. C73 | #12667 | semidirect |
| 130. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626270 | 2 |
| #22626150 | 2 |
| #22625733 | 2 |
| #22624980 | 2 |
| #22611524 | 2 |
| #12667 | 73 |