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. #22620861 | C2 | semidirect |
| 3. #22620670 | C2 | semidirect |
| 4. #22620385 | C2 | semidirect |
| 5. #22609595 | C2 | semidirect |
| 6. #22609589 | C2 | semidirect |
| 7. #22609565 | C2 | semidirect |
| 8. #22609558 | C2 | semidirect |
| 9. #22609537 | C2 | semidirect |
| 10. #22608225 | C2 | semidirect |
| 11. C73×#1705 | C2 | semidirect |
| 195. #1705 | 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 |
| #22620861 | 2 |
| #22620670 | 2 |
| #22620385 | 2 |
| #22609595 | 2 |
| #22609589 | 2 |
| #22609565 | 2 |
| #22609558 | 2 |
| #22609537 | 2 |
| #22608225 | 2 |
| C73×#1705 | 2 |
| #19721 | 73 |