Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
180 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22625089 | C2 | semidirect |
| 3. #22625039 | C2 | semidirect |
| 4. #22625036 | C2 | semidirect |
| 75. C73 | #13641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625089 | 2 |
| C22⋊#14556641 | 2 |
| #22625039 | 2 |
| #22625036 | 2 |
| #22611530 | 2 |
| #13641 | 73 |