Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
442 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22619001 | C2 | semidirect |
| 3. #22608566 | C2 | semidirect |
| 4. #22608477 | C2 | semidirect |
| 5. #22607804 | C2 | semidirect |
| 6. #22607795 | C2 | semidirect |
| 7. C73×#1514 | C2 | semidirect |
| 9. #17988983 | C4 | semidirect |
| 10. #17988963 | C4 | semidirect |
| 11. #17988935 | C4 | semidirect |
| 12. #17988933 | C4 | semidirect |
| 172. #1514 | D73 | semidirect |
| 175. C73 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620665 | 2 |
| #22619001 | 2 |
| #22608566 | 2 |
| #22608477 | 2 |
| #22607804 | 2 |
| #22607795 | 2 |
| C73×#1514 | 2 |
| #9417 | 73 |