Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22619006 | C2 | semidirect |
| 3. #22608440 | C2 | semidirect |
| 4. #22608439 | C2 | semidirect |
| 5. #22607792 | C2 | semidirect |
| 6. #22607759 | C2 | semidirect |
| 7. C73×#1496 | C2 | semidirect |
| 9. #17988963 | C4 | semidirect |
| 10. #17988961 | C4 | semidirect |
| 11. #17988937 | C4 | semidirect |
| 12. #17988933 | C4 | semidirect |
| 183. #1496 | D73 | semidirect |
| 186. C73 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620864 | 2 |
| #22619006 | 2 |
| #22608440 | 2 |
| #22608439 | 2 |
| #22607792 | 2 |
| #22607759 | 2 |
| C73×#1496 | 2 |
| #9281 | 73 |