Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
358 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 21. #17988392 | C4 | semidirect |
| 22. #17988391 | C4 | semidirect |
| 23. #17988390 | C4 | semidirect |
| 24. #358×C73 | C4 | semidirect |
| 174. C73 | #13148 | semidirect |
| 189. #358 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989500 | 2 |
| C2×C16×#64408 | 2 |
| #22626077 | 2 |
| #22626035 | 2 |
| #22624989 | 2 |
| #22624988 | 2 |
| #358×D73 | 2 |
| #13148 | 73 |