Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 14. #17989447 | C4 | semidirect |
| 15. #17989446 | C4 | semidirect |
| 21. #17988717 | C4 | semidirect |
| 23. Q8×#10596831 | C4 | semidirect |
| 25. #17988711 | C4 | semidirect |
| 30. #446×C73 | C4 | semidirect |
| 180. C73 | #8258 | semidirect |
| 184. #446 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊#64408 | 2 |
| #22625432 | 2 |
| #22625313 | 2 |
| #22625145 | 2 |
| #22624827 | 2 |
| #22624821 | 2 |
| #22618862 | 2 |
| #8258 | 73 |