Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 22. #17988966 | C4 | semidirect |
| 23. #17988938 | C4 | semidirect |
| 24. #17988937 | C4 | semidirect |
| 28. #494×C73 | C4 | semidirect |
| 77. #11924036 | Q16 | semidirect |
| 179. C73 | #9290 | semidirect |
| 183. #494 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626724 | 2 |
| #22626115 | 2 |
| #22625447 | 2 |
| #22625365 | 2 |
| #22624785 | 2 |
| #22624756 | 2 |
| #22620875 | 2 |
| #9290 | 73 |