Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
606 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22621806 | C2 | semidirect |
| 3. #22609434 | C2 | semidirect |
| 4. #22609379 | C2 | semidirect |
| 5. #22609177 | C2 | semidirect |
| 6. #22609062 | C2 | semidirect |
| 7. #22608829 | C2 | semidirect |
| 9. C73×#1707 | C2 | semidirect |
| 92. D584 | Q16 | semidirect |
| 168. #1707 | D73 | semidirect |
| 175. C73 | #19927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622835 | 2 |
| #22621806 | 2 |
| #22609434 | 2 |
| #22609379 | 2 |
| #22609177 | 2 |
| #22609062 | 2 |
| #22608829 | 2 |
| C8×D584 | 2 |
| C73×#1707 | 2 |
| #19927 | 73 |