Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. #22625039 | C2 | semidirect |
| 4. #22625038 | C2 | semidirect |
| 5. #22625036 | C2 | semidirect |
| 6. C4×#14556641 | C2 | semidirect |
| 8. #17989520 | C4 | semidirect |
| 9. #17989518 | C4 | semidirect |
| 87. C73 | #13549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989520 | 2 |
| C2×#17989518 | 2 |
| #22625039 | 2 |
| #22625038 | 2 |
| #22625036 | 2 |
| C4×#14556641 | 2 |
| #22611529 | 2 |
| #13549 | 73 |