Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
798 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #22621060 | C2 | semidirect |
| 2. #22620867 | C2 | semidirect |
| 3. #22620670 | C2 | semidirect |
| 4. #22620389 | C2 | semidirect |
| 5. #22609597 | C2 | semidirect |
| 6. #22609588 | C2 | semidirect |
| 7. #22609560 | C2 | semidirect |
| 8. #22609538 | C2 | semidirect |
| 9. #22609519 | C2 | semidirect |
| 10. #22608229 | C2 | semidirect |
| 11. C73×#1716 | C2 | semidirect |
| 192. #1716 | D73 | semidirect |
| 197. C73 | #19721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621060 | 2 |
| #22620867 | 2 |
| #22620670 | 2 |
| #22620389 | 2 |
| #22609597 | 2 |
| #22609588 | 2 |
| #22609560 | 2 |
| #22609538 | 2 |
| #22609519 | 2 |
| #22608229 | 2 |
| C73×#1716 | 2 |
| #19721 | 73 |