Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
448 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #22611625 | C2 | semidirect |
| 4. #22611584 | C2 | semidirect |
| 6. #22609981 | C2 | semidirect |
| 7. C73×#1757 | C2 | semidirect |
| 8. C22×#11924017 | C4 | semidirect |
| 16. #17988625 | C4 | semidirect |
| 17. #17988597 | C4 | semidirect |
| 18. #17988593 | C4 | semidirect |
| 217. #1757 | D73 | semidirect |
| 218. C73 | #13232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619570 | 2 |
| #22611625 | 2 |
| #22611622 | 2 |
| #22611584 | 2 |
| #22611580 | 2 |
| #22609981 | 2 |
| C73×#1757 | 2 |
| #13232 | 73 |