Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610909 | C2 | semidirect |
| 5. #22607821 | C2 | semidirect |
| 6. #22607763 | C2 | semidirect |
| 7. C73×#1485 | C2 | semidirect |
| 10. #17988869 | C4 | semidirect |
| 11. #17988864 | C4 | semidirect |
| 12. #17988794 | C4 | semidirect |
| 13. #17988789 | C4 | semidirect |
| 210. #1485 | D73 | semidirect |
| 213. C73 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619996 | 2 |
| #22619052 | 2 |
| #22610909 | 2 |
| C4×#14556517 | 2 |
| #22607821 | 2 |
| #22607763 | 2 |
| C73×#1485 | 2 |
| #8971 | 73 |