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. #22621055 | C2 | semidirect |
| 2. #22620865 | C2 | semidirect |
| 3. #22620667 | C2 | semidirect |
| 4. #22620389 | C2 | semidirect |
| 5. #22609598 | C2 | semidirect |
| 6. #22609593 | C2 | semidirect |
| 7. #22609562 | C2 | semidirect |
| 8. #22609561 | C2 | semidirect |
| 9. #22609518 | C2 | semidirect |
| 10. #22608225 | C2 | semidirect |
| 11. C73×#1709 | C2 | semidirect |
| 194. #1709 | 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 |
|---|---|
| #22621055 | 2 |
| #22620865 | 2 |
| #22620667 | 2 |
| #22620389 | 2 |
| #22609598 | 2 |
| #22609593 | 2 |
| #22609562 | 2 |
| #22609561 | 2 |
| #22609518 | 2 |
| #22608225 | 2 |
| C73×#1709 | 2 |
| #19721 | 73 |