Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 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. #22618925 | C2 | semidirect |
| 3. #22608541 | C2 | semidirect |
| 4. #22608490 | C2 | semidirect |
| 5. #22608467 | C2 | semidirect |
| 6. #22607830 | C2 | semidirect |
| 7. C73×#1295 | C2 | semidirect |
| 10. #17988996 | C4 | semidirect |
| 11. #17988976 | C4 | semidirect |
| 12. #17988952 | C4 | semidirect |
| 13. #17988947 | C4 | semidirect |
| 215. #1295 | D73 | semidirect |
| 216. C73 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620629 | 2 |
| #22618925 | 2 |
| #22608541 | 2 |
| #22608490 | 2 |
| #22608467 | 2 |
| #22607830 | 2 |
| C73×#1295 | 2 |
| #9432 | 73 |