Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #22608526 | C2 | semidirect |
| 5. #22607824 | C2 | semidirect |
| 6. #22607804 | C2 | semidirect |
| 7. C73×#1506 | C2 | semidirect |
| 10. #17988879 | C4 | semidirect |
| 11. #17988874 | C4 | semidirect |
| 12. #17988794 | C4 | semidirect |
| 13. #17988789 | C4 | semidirect |
| 199. #1506 | D73 | semidirect |
| 202. C73 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620087 | 2 |
| #22618943 | 2 |
| #22609742 | 2 |
| #22608526 | 2 |
| #22607824 | 2 |
| #22607804 | 2 |
| C73×#1506 | 2 |
| #9159 | 73 |