Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #22619880 | C2 | semidirect |
| 4. #22610916 | C2 | semidirect |
| 5. #22610031 | C2 | semidirect |
| 6. #22607838 | C2 | semidirect |
| 231. C73 | #9936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620737 | 2 |
| #22619880 | 2 |
| #22615721 | 2 |
| #22610916 | 2 |
| #22610031 | 2 |
| #22607838 | 2 |
| C73×#1507 | 2 |
| #9936 | 73 |