Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22610764 | C2 | semidirect |
| 3. #22608654 | C2 | semidirect |
| 4. #22608440 | C2 | semidirect |
| 5. C73×#1536 | C2 | semidirect |
| 7. #17989303 | C4 | semidirect |
| 10. #17989222 | C4 | semidirect |
| 14. #17988611 | C22 | semidirect |
| 16. #17988433 | C22 | semidirect |
| 21. #432×C73 | C22 | semidirect |
| 158. #1536 | D73 | semidirect |
| 160. C73 | #8491 | semidirect |
| 170. #432 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624336 | 2 |
| #22610764 | 2 |
| #22608654 | 2 |
| #22608440 | 2 |
| C73×#1536 | 2 |
| #8491 | 73 |